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ECONOMICS  OF  BRIDGEWORK 

A  SEQUEL  TO  BEIDGE  ENGINEERING 


BY 

J.  A.  L.  WADDELL 


?..Q 


C.E.  (Rens.  Poly.  Inst.);  B.A.Sc,  Ma.E.,  D.Sc.  (McGill  Univ.);  D.E. 

(Univ.  of  Neb.);  LL.D.  (Univ.  of  Mo.);  Kogakuhukushi 

(Doctor  of  Eng.,  Imp.  Univ.  of  Japan) 

Correspondant  de  I'lnstltut  de  France  dans  I'Academle  des  Sciences;  Corresponsal  de  la  Socledad  de  Ingenleroa  del 
Peru;  Knight  Commander  of  the  Japanese  Order  of  the  Rising  Sun;  Membre  de  la  Soclete  de  Blenfalsance  de  la 
Grande  Duchesse  OlgadeRussle;  Consulting  Engineer,  New  York  City;  Member  of  the  American  Society 
of  Civil  Engineers;  of  the  American  Institute  of  Consulting  Engineers;  of  the  Franklin  Institute;  of 
the  Institution  of  Civil  Engineers,  London;  of  La  Soclete  des  Ingenleurs  CIvlls,  Paris;  of  the  En- 
gineering Institute  ot  Canada;  of  the  Western  Society  of  Engineers;  of  the  Rensselaer  Society 
of  Engineers;    of  the  Society  for  the  Promotion  of  Englqeerlng  Education;    of  the 
American  Association  for  the  Advancement  of  Science;  of  the  American  Society  for 
Testing  Materials;  of  the  International  Society  for  Testing  Materials;  of  the 
American  Railway  Engineering  Association;  of  La  Soclete  de  Geographic 
de  France;  ot  the  Phi  Beta  Kappa  Society;     of  the  Tau  Beta  Pi 
Society;  of  the  Sigma  XI  Society;  of  the  National  Conservation 
Association;    of  The  National  Economic  League;    and  Hon- 
orary Member  of  the  Engineers'  Club  of  Kansas  City; 
and  of  the  Soclete  Internationale  d'Etudes 
de  Correspondance  et  d'Echangea 
"  Concordia," 
Paris 


BOSTOK  COLLEGE  LIBRART 
CHESTJSUT  HILL,  MASS» 


NEW  YORK 

JOHN    WILEY    &    SONS,    Inc 

London:  CHAPMAN  &  HALL,  Limited 

1921 


Copyright.  1921.  by 
J.  A.  L.  WADDELL 


^ 


^ 


PRESS  or 

ORAUNWOHTH  I.  CO. 

•OOK  MANUFACTUHIRS 

■ROOKLVN,  N.  V. 


TO  THE 
OF 

f  Ittatitttt  U  Jlrante 

THE  UNIVERSALLY  ACKNOWLEDGED 

LEADER  OF  THE   WORLD 

IN    ALL   LINES    OP    SCIENTIFIC    THOUGHT 

AS  A  MARK  OP 

THE  AUTHOR'S  GRATEFUL   APPRECIATION  OP  THE 

PROUD  DISTINCTION  CONFERRED  UPON  HIM 

BY  FRANCE 

THROUGH  ADMISSION  TO  ITS  RANKS 

ON    DECEMBER    16.    1918. 

AND  AS  AN  EVIDENCE  OP  HIS  PROPOUIvD  ADMIRATION 

AND  REGARD  FOR  THE  ENTIRE   FRENCH   NATION 

THIS  TREATISE 

HIS  FINAL  CONTRIBUTION  IN  BOOK  FORM 

TO  ENGINEERING  LITERATURE 

WITH  THE  academy's  KIND  PERMISSION 

IS   MOST   RESPECTFULLY 

.     DEDICATED 


PREFACE 


The  author's  object  in  foisting  still  another  bridge  book  upon  his  long- 
suffering  brother  engineers  is  twofold,  viz.: 

First.  A  desire  to  leave  behind  him  for  the  benefit  of  the  next 
generation  of  bridge  speciahsts,  in  shape  readily  available 
for  use,  a  solution  of  all  the  major  economic  problems  in 
bridge  work  and  an  extensive  treatment  of  most  of  the  minor 
ones.  He  has  endeavored  to  cover  every  possible  economic 
question  of  importance;  and,  if  any  such  be  omitted,  it  is 
because  he  did  not  recognize  their  existence.  To  what 
extent  he  has  succeeded  in  this  endeavor  can  be  determined 
only  by  the  reception  which  the  book  meets  from  the 
engineering  profession. 

Second.  To  show  to  specialists  in  all  branches  of  the  engineering 
profession  the  type  of  book  on  economics  which,  in  his 
opinion,  each  specialty  needs  and  how  broad  and  thorough, 
if  possible,  should  be  the  treatment  of  the  subject. 

The  author  feels  that  he  is  the  logical  person  to  write  a  book  upon  the 
economics  of  bridgework,  because  he  has  been  investigating  the  matter  for 
thirty-seven  years,  and  has  dealt  at  length,  upon  more  than  twenty  different 
occasions,  in  books,  pamphlets,  and  memoirs,  with  various  economic  topics 
on  the  subject  of  bridge  designing,  as  can  be  seen  by  referring  to  the  list  of 
the  said  writings  given  in  the  Appendix. 

An  explanation  but  not  an  apology  is  needed  for  the  fact  that  certain 
portions  of  "Bridge  Engineering"  have  been  copied  in  a  few  of  the  chap- 
ters. As  that  work  from  start  to  finish  is  impregnated  with  the  funda- 
mental idea  of  economy,  and  as  this  book  is  intended  to  cover  the  entire 
field  of  bridge  economics,  it  was  necessary  to  include  herein  the  gist  of  all 
that  appears  on  the  matter  in  that  work,  as  well  as  the  substance  of  all  the 
author's  economic  writings  that  are  subsequent  to  its  publication.  Wher- 
ever an3^hing  previously  written  on  the  subject  could  advantageously  be 
modified  or  enlarged,  this  has  been  done;  but  where  it  could  not  be  im- 
proved upon  or  augmented,  the  only  thing  to  do  was  to  copy  it  verbatim. 
Hence,  should  any  reader  see  any  portion  of  "Economics  of  Bridgework," 
which  appears  familiar  to  him,  if  he  has  read  this  preface  he  will  under- 
stand the  reason  therefor  and  will,  the  author  trusts,  excuse  the  occurrence. 

V 


VI  PREFACE 

In  proof  of  the  previous  statement  that  the  treatment  throughout 
"Bridge  Engineering"  is  based  on  the  conception  of  economics,  there  is 
offered  the  following  extract  from  a  review  of  that  work  written  by  Albert 
Reichmann,  Mem.  Am.  Soc.  C.E.,  and  pubHshed  in  the  October,  1916, 
issue  of  the  Journal  of  the  Western  Society  of  Engineers. 

"In  a  larger  sense,  this  work  is  a  treatise  on  the  subject  of  'Economics 
of  Bridge  Engineering.'  This  train  of  thought  can  be  traced  throughout 
the  entire  work,  all  subjects  being  treated  fully  and  in  a  broad  way,  and 
with  the  idea  of  value  constantly  brought  out." 

There  is  a  salient  feature  of  the  present  book  to  which  attention  should 
be  called,  and  that  is  the  scarcity  of  treatment  of  economic  problems  by 
pure  mathematics,  nearly  all  the  form_ulse  given  being  semi-rational,  semi- 
empirical.  The  reason  for  this  is  that  the  conditions  affecting  most  of  the 
economic  questions  in  bridge  designing  are  far  too  complicated  to  lend 
themselves  to  solution  by  mathematical  manipulations.  This  fact  has  not 
always  been  recognized  by  engineering  writers;  for,  during  the  last  three  or 
four  decades,  numerous  attempts  have  been  made  to  settle  important  eco- 
nomic bridge-problems  mathematically,  with  the  result  that  the  conclusions 
thus  drawn  have  proved  to  be  erroneous  and  generally  totally  useless. 

It  is  prognosticated  that,  in  the  future,  there  will  be  no  such  fundamental 
changes  in  methods  of  bridge  design  and  construction  as  to  render  really 
incorrect  the  numerous  economic  conclusions  reached  herein;  because 
bridge  building  has  now  become  fairly  well  systematized.  About  the  only 
important  change  in  sight  is  the  adoption  of  high-alloy  steel  for  long-span 
superstructures;  and  the  effects  of  this  have  been  duly  anticipated.  The 
reasons  for  this  belief  are  that  the  investigations  upon  which  the  book  is 
based  were  in  general  predicated  upon  fundamental  engineering  principles 
that  do  not  vary;  and  that  the  effects  of  possible  changes  in  unit  prices  of 
materials  in  place  and  in  other  general  conditions  affecting  design  have  been 
indicated.  While  it  is  true  that  an  abnormal  variation  of  a  temporary 
nature  in  the  unit  price  of  some  important  material  of  bridge  construction, 
some  pecuhar  feature  of  structure-location  affecting  erection,  or  possibly 
some  other  cause,  may  change  somewhat  the  findings  stated  herein,  it  must 
be  remembered  that,  as  pointed  out  in  several  places,  up  to  a  certain  limit  a 
considerable  divergence  from  the  exact  economic  condition  will  usually 
cause  no  serious  augmentation  of  total  cost.  This  is  the  saving  clause 
which  Hinders  the  author's  economic  conclusions  sufficiently  dependable 
for  th(;  future  as  well  as  for  the  present. 

The  story  of  the  writing  of  this  treatise  is  as  follows: 

In  the  summer  of  1916,  when  "Bridge  Engineering"  was  issued,  the 
author  recognized  that  there  was  one  very  important  bridge  subject  that 
he  had  not  completely  covered,  viz.,  economics;  and  he  thereupon  listed 
ten  major  e(;onomic  pro])loms  at  tliat  time  unsolved,  and  came  to  the  deter- 
mination that  they  should  no  longer  be  left  in  that  condition,  if  he  could 
prevent  it.     After  repeatedly  failing  to  interest  any  other  investigator  in 


PREFACE  Vll 

the  matter,  he  himself  undertook  the  task  and  accomphshed  it,  at  least  to 
his  own  satisfaction,  in  four  years  of  hard  work. 

The  following  is  a  hst  of  the  said  economic  questions  arranged  in  the 
order  of  their  final  solution: 

1.  Economics  of  Steel  Arch-Bridges. 

2.  Comparative  Economics  of  Cantilever  and  Suspension  Bridges. 

3.  Economic  Span-Lengths  for  Simple-Truss  Bridges  on  Various 
Types  of  Foundation. 

4.  Possibilities  and  Economics  of  the  Transbordeur. 

5.  Comparative  Economics  of  Continuous  and  Non-Continuous 
Trusses. 

6.  Comparative  Economics  of  Wire  Cables  and  High-Alloy-Steel 
Eye-bar-Cables  for  Long-Span  Suspension-Bridges. 

7.  Economics  of  Reinforced-Concrete,  Steam-Railway  Bridges. 

8.  De  VEmploi  Economique  des  Alliages  d.Acier  dans  la  Construction 
des  Fonts. 

9.  Bridge  Versus  Tunnel  for  the  Proposed  Hudson  River  Crossing 
at  New  York  City. 

10.  Economics  of  Movable  Spans. 

As  fast  as  these  economic  investigations  were  finished,  they  were 
separately  incorporated  in  chapters  of  this  book,  occasionally  in  toto  but 
generally  with  slight  modifications  or  omissions. 

In  the  preparation  of  a  few  portions  of  the  manuscript,  the  author  has 
received  valuable  assistance  from  the  following  engineers,  to  whom  he 
herewith  tenders  his  hearty  thanks:  Messrs.  Thomas  E.  Brown,  Leon  L. 
Clarke,  Watson  Vredenburgh,  Thomas  Earle,  C.  M.  Canady,  Harry  K. 
Seltzer,  Joseph  J.  Yates,  Frank  W.  Skinner,  Charles  F.  Loweth,  Carl  S. 
Heritage,  J.  G.  Chalfant,  Vernon  R.  Covell,  Edward  A.  Byrne,  J.  B.  W. 
Gardiner,  L.  H.  Beach,  P.  S.  Bond,  A.  H.  Sabin,  and  Shortridge  Hardesty. 

The  special  portions  of  the  book  whereon  these  gentlemen  have  aided 
are  indicated  throughout  the  text,  excepting  in  the  case  of  the  author's 
assistant  engineer,  Mr.  Hardesty,  who  helped  with  certain  of  the  cal- 
culations and  gave  the  entire  treatise  a  general  check. 

It  may  be  of  interest  to  some  readers  to  learn  how  Chapter  XLIV  on 
"Economics  of  Military  Bridging"  happened  to  be  included  in  the  book; 
for  it  is  a  subject  concerning  which,  before  the  said  chapter  was  written, 
the  author  knew  practically  nothing.  Incidentally  it  came  to  the  atten- 
tion of  Major  R.  W.  Lewis — a  young  engineer  who  served  with  distinction 
in  the  American  Army  on  the  battle  fields  of  France,  and  a  son  of  Col.  I.  N. 
Lewis,  the  famous  inventor  of  the  machine  gun  which  bears  his  name,  and 
which  so  greatly  aided  the  Allies  in  winning  the  war — that  this  book  was  in 
course  of  preparation.  He  thereupon  called  on  the  author  and  asked  if  he 
would  consider  favorably  a  suggestion  to  insert  in  the  treatise  a  chapter 
prepared  officially  by  the  Engineer  Corps  of  the  Army  on  the  subject  of 


VIU  PREFACE 

economics  of  military  bridgework.  Upon  receiving  an  acquiescent  reply, 
Major  Lewis  proceeded  to  the  Capital,  consulted  Major  General  Beach, 
the  Chief  of  Engineers,  and  made  a  Uke  suggestion  to  him.  The  result 
was  that  the  General  agreed  to  write  a  "Foreword"  for  the  chapter,  and 
detailed  Col.  P.  S.  Bond,  in  consultation  with  some  of  his  brother  officers, 
to  do  the  writing.  The  author  deems  the  outcome  an  exceedingly  valuable 
addition  to  his  book;  and  he  hopes  that  many  of  his  readers,  in  consequence 
of  its  perusal,  will  be  induced  to  take  such  an  interest  in  mihtary  bridge 
engineering  as  to  ensure  that  they  shall  be  better  prepared  to  serve  our 
country  in  case  of  war  than  were  most  of  the  civilian  engineers  when  the 
call  to  arms  came  in  1917. 

It  is  intended  that  this  shall  be  the  last  technical  book  which  the  author 
will  ever  write,  for  reasons  explained  in  the  concluding  chapter;  and  he 
hopes  that  it  and  its  immediate  predecessor,  "Bridge  Engineering,"  wiU, 
for  many  a  year  to  come,  prove  of  real  service  to  the  engineers  of  his 
specialty,  in  the  advancement  of  which,  almost  ever  since  graduation 
forty-five  years  ago,  he  has  taken  an  intense  and  absorbing  interest. 


CONTENTS 


PAGE 

Preface • v 

Table  op  Contents .        ix 

List  of  Illustkations xxvii 

List  of  Tables xxxi 


CHAPTER   I 

INTRODUCTION 

Necessity  for  general  application  of  principles  of  economics. — Labor  a  blessing — 
not  a  curse. — Love  for  one's  work  a  requisite. — ^Business  opportunity  of 
U.  S.  A.  being  lost. — Necessity  for  Americans  to  work  harder  and  more 
efficiently. — Increasing  national  efficiency  through  application  of  economic 
principles. — Importance  of  the  work  of  the  engineer  and  increasing  his 
efficiency. — Teaching  economics  in  technical  schools. — Report  of  Committee 
of  S.P.E.E.  on  "The  Study  of  Economics  in  Technical  Schools." — Sug- 
gested treatise  on  "Economics  of  Engineering." — Author's  lectures  on 
"Engineering  Economics"  at  University  of  Kansas. — -Author's  failure  to  in- 
terest others  in  proposed  treatise  on  "Economics  of  Engineering." — Presen- 
tation of  this  book  as  a  sample  of  what  is  needed  in  all  engineering  specialties. 


CHAPTER   II 

GENERAL  ECONOMIC   PRINCIPLES 

Literature  on  Engineering  Economics  very  meagre. — Definition  of  "Economics." — 
General  economic  principle. — Economics  of  proposed  enterprises. — Experi- 
ence requisite  for  making  economic  investigations. — -Complication  of  economic 
investigations. — Example  of  economic  study  for  proposed  bridge  across 
San  Francisco  Harbor. — Short-sightedness  of  promoters. — ^Glaring  example 
of  failure  for  want  of  economic  study. — ^Economic  study  for  proposed  bridge 
over  Mississippi  River  near  New  Orleans. — Economic  study  for  replacement 
of  a  bridge  over  the  Mississippi  River. — Method  for  comparing  the  economics 
of  several  methods  of  accomplishing  the  same  result. — Method  of  contrasting 
several  differing  types  of  construction. — ^Mathematical  treatment  of  economic 
comparison. — Special  conditions  precluding  adoption  of  most  economic 
method  of  procedure. — Anticipating  the  future. — First  cost. — Systemization. 
— Time  versus  materials. — Labor  versus  materials. — Compensating  factors  in 
economic  comparisons  and  frequent  wide  range  of  economic  limits. — 
Economic  variation  with  live  loads. — Recording  diagrams. — Economics  of 
mental  effort. — Labor 6 


X  CONTENTS 

CHAPTER  III 
ECONOMICS  OF  THE   PROMOTION   OF  BRIDGE   PROJECTS 

PAGE 

Promoter's  inflated  ideas. — Keeping  down  first  cost. — -Traffic  investigation. — 
Revenue  investigation. — Maintenance  and  repairs. — Determination  re 
undertaking  the  proposed  venture. — Pedestrian  traffic. — Initial  temporary 
economic  expedients. — Constructions  part  permanent  part  temporary.  —East 
Omaha  Bridge, — Growing  scarcity  of  timber 20 

CHAPTER   IV 

EFFECT  ON  ECONOMICS  FROM  VARIATIONS  IN  MARIvET  PRICES 
OF  LABOR   AND   MATERIALS 

Comparative  unimportance  of  market  price  variations. — Structural  metal  price 
variations. — Cement  price  variations. — Monograph  on  "Economic  Span- 
lengths  for  Simple-truss  Bridges  on  Various  Types  of  Foundation." — Sus- 
pension-bridge price- variations. — Location  affecting  economic  layout.   .      .       23 

CHAPTER  V 

ECONOMICS   OF  ALLOY  STEELS 

Three  fundamental  conditions  affecting  economic  question. — Economic  criterion 
for  rods  or  bars. — Economic  criterion  for  plate-girder  spans. — Economic  cri- 
terion for  long  spans. — Examples  computed. — How  economic  curves  were 
established. — Extension  of  economic  curves  into  "speculative  zone." — 
Cutting  out  carbon  steel  entirely  in  very-long-span  bridges. — Accuracy  of 
the  curves. — General  applicability  of  curves  for  all  cases. — Use  of  alloy  steel 
for  bridgework  in  its  infancy. — ^Author's  investigation  on  "Nickel  Steel  for 
Bridges." — -Present  great  demand  for  nickel  prohibits  use  in  bridges. — 
Other  alloys  of  steel  for  bridgework. — High-carbon  steel  not  advisable  for 
bridges. — Mayarl  Steel. — Vanadium  steel. — Silicon  steel. — "Purffied  steel." 
— Aluminum  steel. — Molybdenum  steel. — Nichromol  steel. — Improvement 
by  French  scientists  on  Bessemer  process. — Study  on  economics  of  molyb- 
denum steel  for  bridgework. — Catalogue  re  "  Molybdenum  Commercial 
Steels." — Proposed  nomenclature  for  various  molybdenum-steel  alloys. — 
Legitimate  working  intensities  for  molybdenum  steel  alloys. — Moa^reness 
of  data. — Heat-treated  chrome  steel  with  and  without  molybdenum. — Heat- 
treated  chrome-nickel  steel  with  and  without  molybdenum. — Ileat-troated 
chrome-vanadium  steel  with  and  without  molybdenum. — Heat-treated  nickel 
steel  with  and  without  molybdenum. — Heat-treated  carbon  steel  with 
molybdenum. — Untreated  and  treated  chrome  steel  with  molybdenum. — 
Assumed  unit  prices  erected  for  alloy  steels. — Best  drawing  temperature  for 
alloy  steels  in  bridgework. — Carmol  steel  versus  carbon  steel. — Chromol 
steel  versus  vhromo,  steel.  Nicmol  steel  versus  nickel  steel. — Nichromol  steel 
versus  nichro  steel. — Chrovanmol  steel  versus  chrovan  steel.  Best  per- 
centage of  molybdenum  for  alloy  steels  in  bridgework. — Comi)ilation  of 
results. — Most  i)romisiiig  molybdenum  alloy  for  bridge  steel 26 


CONTENTS  XI 

CHAPTER  VI 

COMPARATIVE  ECONOMICS  OF  BRIDGES  AND  TUNNELS 

PAGE 

Difficulty  of  comparison. — Must  be  between  one  bridge  and  several  tunnels. — ■ 
Traffic  in  tunnels. — Ventilation  of  traffic  tunnels. — Comparative  agreeable- 
ness  of  passage  by  bridge  and  tunnel. — Comparative  extents  of  climbing  ia 
bridges  and  tunnels. — Comparative  costs. — Bridge  versus  Tunnel  for  the  Pro- 
posed Hudson  River  Crossing  at  New  York  City. — Desirability  of  methods 
of  handUng  traffic  across  the  river. — Cost  of  operation. — Time  expenditures. 
— ^Agreeableness. — Sanitation. — Ventilation. — Carbon  monoxide  danger.— 
Approach  grades  used  in  the  comparison. — Tunnel  estimates.  —  Variation  of 
cost  of  tubes  with  diameter. — Comparative  cost  of  a  double- track  tube  and 
two  single-track  tubes. — Unit  prices  for  bridge  materials  in  place. — Limi- 
tation of  cost  by  efficiency  instead  of  aesthetics. — Cost  diagram  for  bridges 
and  tunnels. — Description  of  contrasted  structures. — Fairness  of  com- 
parison.— Cost  of  right-of-way  and  property  damages. — Spiral  approaches. — 
Table  of  total  costs  of  bridges  and  tunnels. — Conclusion  as  to  the  compara- 
tive economics. — Temporary  combination  of  bridge  and  tunnels. — Sugges- 
tion for  further  study  of  proposed  crossing  before  committing  the  pubUc  to  the 
present  policy 53 

CHAPTER  VII 

COMPARATIVE  ECONOMICS  OF  HIGH-LEVEL  AND  LOW-LEVEL 

CROSSINGS 

Definition  of  terms. — Comparison  generally  a  matter  of  expediency  instead  of  one 
of  economics. — Using  one  through  span  over  channel  and  making  all  other 
spans  deck  structures. — Advantages  and  disadvantages  of  the  two  types. — 
Approximate  average  figures  of  comparative  costs. — Capitalization  of  various 
aimual  expenditures. — Power-cost  capitaHzation  unnecessary 61 

CHAPTER  VIII 

COMPARATIVE  ECONOMICS  OF  STEEL  AND  REINFORCED- 
CONCRETE  STRUCTURES 

Difficulty  in  making  comparison. — Variation  in  market  prices  an  important  factor. 
— Must  consider  factors  of  maintenance  and  repairs. — Greater  popularity  of 
concrete  structures  among  non-technical,  iminitiated  people. — -Comparative 
limits  of  life. — Personal  equation. — Science  of  reinforced-concrete-bridge 
designing  not  yet  so  highly  developed  as  that  of  steel-bridge  designing. — 
^Esthetics  affects  costs  of  reinforced-concrete  bridges. — Live  load  affects  the 
economic  comparison. — Designing  by  inexperienced  computers. — Variation 
in  costs  of  excavation  for  foundations. — Quick  method  of  settling  this  eco- 
nomic question. — Practicable  limit  of  span-length  for  reinforced-concrete 
bridges. — Settlement  of  arches  during  construction. — Effect  of  height  of 
crossing  upon  the  economic  comparison. — Unavoidable  generality  of  treat- 
ment of  subject  and  reasons  therefor. — Impracticable  to  reach  any  fixed  or 
reliable  conclusion 64 


XIV  CONTENTS 

PAGE 

emment  requirements. — Rules  somewhat  elastic. — Location  of  movable  span. 
— Grade  and  alignment. — Curvature  on  approaches. — Skew  crossings. — Geo- 
graphical conditions. — Commercial  influences. — Proposed  bridge  at  Second 
Narrows,  Vancouver,  B,  C. — ^Property  considerations. — General  features  of 
structure. — Character  of  movable  span. — Shore  protection.— Future  enlarge- 
ment.— Time  considerations. — Stream  conditions. — Passing  drift  and  ice. — 
Clear  waterway  for  probable  maximum  flood. — Shifting  of  channel. — 
Foundation  considerations. — Navigation  influences. — Construction  facilities. 
— ^Erection  considerations. —  ^Esthetics. — Maintenance  and  repairs. — Theo- 
retical economics. — Conclusion .,,,..     116 

CHAPTER  XVI 

ECONOMICS   OF   LOADS   AND  UNIT  STRESSES 

Importance  of  economic  determination  of  live  load. — Occasional  excess  live  load- 
ings.— Modern  truck  loadings. — ^Decrease  of  live  load  with  span-length. — 
Electric-railway  car  loads. — Standard  steam-railway  loadings. — Electric-rail- 
way loadings. — Highway  loadings. — Loadings  for  cantilevers. — Impact  load- 
ings.— Widths  for  roadways. — Three-line-travel  decks  are  unsatisfactory. — 
Footwalk  widths. — Pedestrian  trafiic. — Gauntleted  tracks. — Economic 
arrangement  of  decks  to  accommodate  several  kinds  of  traffic. —  Combined- 
railway-and-highway-bridge  traffic. — Screens. — Division  of  combined 
bridges  into  six  classes  and  dissertation  concerning  economics  of  each 
class. — Author's  Sioux  City  Bridge. — Author's  East  Omaha  Bridge. — 
Author's  Eraser  River  Bridge  at  New  Westminster,  B.  C. — Design  for 
Second  Narrows  Bridge  over  Burrard  Inlet  at  Vancouver,  B.  C. — Author's 
Fratt  Bridge  at  Kansas  City. — Keeping  live  loads  down  to  least  legitimate 
limits. — ^Extreme  and  illegitimate  reduction  of  live  loads. — Determination 
of  unit  stresses. — High-carbon  steel  not  good  for  reinforcing  bars. — In  frequent 
loadings  permit  live-load  reduction. — Fallacy  of  abnormally  high  live  loads 
and  correspondingly  greater  unit  stresses. — Selection  of  live  load  important 
for  very-long- span  bridges. — Forced  increase  in  unit  stresses. — Skimping  of 
details. — Combination  of  stresses  in  trestles. — Increments  of  intensities 
for  various  combinations  of  stresses,  and  dissertation  on  the  economics 
involved. — Impracticability  of  eliminating  entirely  the  personal  equation  in 
trestle  designing. — Combination  of  stresses  in  cantilever  bridges  and  arches. 
— Caution  against  inadvertently  adding  stresses  of  opposite  kinds. — Com- 
bination of  stresses  of  opposite  kinds. — Conclusion  re  best  policy  for 
combining  reversing  stresses. — Combinations  of  live  and  dead-load  stresses 
with  secondary  stresses. — Proper  relation  between  intensities  of  working 
stresses  in  tension  and  compression. — Report  of  the  Committee  on  Column 
Tests  of  the  A.S.C.E.  and  author's  comment  thereon  in  Engineering  News 
Record. — Suggested  tests  of  members  when  actually  in  full-size  bridges.  .     .     125 

CHAPTER  XVII 

ECONOMICS  OF  TIME  AND  MONEY  IN  MAKING  COST  ESTIMATES 

FOR  BRIDGES 

Value  of  data  in  "Bridge  Engineering"  for  making  bridge  estimates  expeditiously. 
— Four  problems  in  economic  estimating  set  for  solution  in  a  competition 


CONTENTS  XV 

PAGE 

between  students  of  technical  schools. — Tests  made  by  the  author  of  the 
"B.  E. "  methods  of  making  quick  cost-computations  in  bridgework. — 
Eleven  examples  solved  in  the  making  of  quick  estimates. — Quick  estimates 
for  suspension  bridges. — Statement  of  the  student  problems 141 

CHAPTER  XVIII 

ECONOMIC  SPAN-LENGTHS  FOR  SIMPLE-TRUSS  BRIDGES  ON 
VARIOUS  TYPES  OF   FOUNDATION 

But  little  known  previously  concerning  true  economic  span-lengths  for  varying 
substructure  conditions. — Author's  mathematical  solution  of  three  decades 
ago  and  its  limitations. — Special  investigation  made  by  actual  estimates  of 
cost  of  over  two  hundred  piers  with  their  spans. — -Instigation  of  the  inves- 
tigation was  the  series  of  studies  for  the  proposed  New  Orleans  bridge. — ■ 
Assumptions  and  conditions  for  investigation. — -Character  of  structures. — ■ 
Methods  of  pier  sinking. — ^Specifications  for  designing. — -Loads. — Per- 
missible pressures  on  soil  and  piles. — Unit  prices  of  materials  in  place. — 
Method  of  determining  the  economic  span-length. — Recording-diagrams 
and  table. — Resume  of  results  of  computations. — Deductions. — Check  on 
old  method  of  determining  economic  span-lengths. — -Relative  weights  of 
metal  in  equal-truss,  three-span  bridges  and  structures  of  the  same  kind, 
same  total  length,  and  same  loading,  but  having  the  central  span  lengthened 
and  the  other  two  equally  shortened ,     150 


CHAPTER  XIX 

ECONOMICS   OF  SUBSTRUCTURES 

Old  method  of  designing  masonry  piers. — Author's  experience  in  designing  piers 
for  Red  Rock  Cantilever  bridge. — Day  of  cut-stone-masonry  piers  is  past. — ■ 
Copings. — Economics  of  reinforcing  for  traction  effects. — Dumb-bell  piers. — 
Hollow  shafts  to  reduce  load  on  foundations. — Piers  composed  of  two  cyl- 
inders.— Mattresses. — Temporary  piers. — Cocked  hat. — -Cutting  down  and 
rebuilding  of  main  piers  of  the  Fratt  Bridge  at  Kansas  City. — Ice-breakers. — 
Reinforced-concrete  versus  timber  for  cribs  and  caissons  of  bridge  piers. — 
Steel  versus  timber  for  concrete  forms. — Best  depth  to  carry  pier-shaft  below 
low-water  mark. — Reduction  of  pier  size  to  avoid  lessening  the  area  of  Avater- 
way. — Clearance  in  crib  around  base  of  shaft. — Pneumatic  process  versus 
open-dredging. — Coffer-dam  method  versus  open-dredging. — Comparative 
economics  of  open-dredging  caisson  and  pile-filled  crib. — Economics  of 
employing  both  the  pneumatic  and  the  open-dredging  processes  on  the  piers 
for  same  bridge. — Economics  of  hastening  pier  sinking. — -Comparative 
economics  of  stepping  off  plain-concrete  bases  or  spreading  suddenly  by 
using  reinforcing  bars. — Reinforced  concrete  piles  versus  wooden  ones.        .      167 

CHAPTER  XX 

ECONOMICS  OF  TRUSSES  AND   GIRDERS 

This  problem  cannot  be  solved  by  complicated  mathematics,  but  only  by  making 
actual  competitive  designs  and  estimates  of  cost. — Mathematical  solution 
of   economic   truss-depths. — Economic   depths   of  plate-girder   spans   and 


XVI  CONTENTS 


beams. — True  economic  investigation  for  plate-girders. — Considerations 
tending  to  offset  the  advantage  of  employing  economic  web-depth. — Old 
rule  of  making  weight  of  flanges  equal  to  that  of  web  and  its  stiffening  is  just 
about  right. — Economic  panel-lengths. — Comparative  economics  of  Warren 
with  Pratt  and  Petit  trusses. — Economic  limiting  span-lengths  for  polygonal 
chords 175 

CHAPTER  XXI 

ECONOMICS   OF   DECKS   AND   FLOOR-SYSTEMS 

Possible  types  of  deck  for  railway  bridges. — -Open-floor. — Trough  floor. — Bal- 
lasted decks. — Ballast  resting  directly  on  steel  plate. — Ballast  resting  on 
reinforced-con Crete  slab. — Resting  ties  on  bottom-flange  angles  or  on  special 
shelf-angles. — Depth  and  number  of  beams  and  stringers. — Encasing  the 
said  beams  in  concrete. — Floor  systems. — Standard  floor  system. — Jack- 
stringers  versus  fom-  lines  of  carrying  stringers  per  track. — Economic  panel 
length. — Cut-away  ends  of  floor-beams. — Economic  depths  for  stringers. — 
Economic  depths  for  floor-beams. — -Effect  on  economics  of  under-clearance 
requirements. — Floors  for  half-through,  plate-girder  spans. — -Economic  spac- 
ing of  deck  trusses  for  double-track  bridges. — Electric-raU^^ay  bridges. — 
Highway-bridge  decks. — Timber  deck  versus  concrete  deck. — Danger  to 
timber  deck  from  fire. — Deck  for  bascule  bridges. — Pavings  for  roadways. — 
Plank  floors. — Creosoted  planks. — ^Concrete  base. — Wooden  block  pave- 
ment.— Brick  pavement. —  Asphalt  and  bituminous  pavements. — Concrete 
wearing  surface. — -Sidewalks. — ^Sub-paving  or  base. — Curbs. — Handrails. — • 
Electric-railway  tracks. — Floor  systems. — Spaqing  of  I-beams. — Omission 
of  floor-system  in  deck  spans.— Economic  number  of  girders  in  deck,  plate- 
girder  spans. — Standard  floor-system  in  deck,  plate-girder  spans. — Stringer 
spacing. — Sidewalk  slabs. — Number  of  girders  in  half-through  spans. — 
Stringerless  floor  vers^ls  floor  with  stringers. — Cantilever  brackets. —  Floor 
of  minimum  weight. — Stiffened-buckle-plate  floor. — Haydite  concrete.        .      182 

CHAPTER  XXn 

GENERAL  ECONOMICS   OF   DESIGNING   AND   DETAILING 

Simple  details  are  economic. — Carry  stresses  by  shortest  route. — Reduction  of 
number  of  rivet  holes  in  a  section  to  a  minimum. — Largest  practicable  radii 
of  gyration  for  compression  members. — H  sections  for  posts. — Compression 
members  carrying  shear. — Non-use  of  cover  plates  in  railway,  deck,  plate- 
girder  spans. — Batten  plates. — Turning  flanges  of  post  channels  in. — Must 
consider  all  panels  of  compression  chord  simultaneously  when  designing 
any  length  thereof. — Use  metal  to  best  advantage  in  detailing. — False 
economy  to  skimp  details. — Details  and  joints  frequently  defy  exact  analysis. 
— Consider  i)ossiblc  rusting  when  detailing. — All  parts  to  be  easily  accessible 
to  paint  brush.  199 

CHAPTER  XXni 

ECONOMICS   IN   DESIGN   FOR  SHOP   CONSIDERATIONS 

Designs  to  be  made  so  as  to  facilitate  shopwork. — Sub-i)imcliiiig  ;\ii(l  reaming 
versus  imiiching  full  size. — Drilling  solid. — Sheared  edges. — End  stiffencrs 


CONTENTS  XVll 

PAGE 

must  not  be  omitted. — Turning  in  flanges  of  channels. — Batten  plates 
inside  of  the  gussets. — Girders  of  constant  or  varying  depths  for  viaducts. — 
Location  of  pedestal  pins. — Non-omission  of  end  floor-beams. — Single 
angles  not  to  be  used  in  tension.— Exact  location  of  top-chord  pins. — Cast 
iron  in  bridges. — Insertion  of  casting  between  foot  of  column  and  the 
masonry. — Variation  in  pound  prices  for  different  sections  of  metal. — Avoid 
special  material. — Adhere  to  standard  sizes. — Design  to  avoid  all  unnecessary 
shopwork. — ^Reaming  to  templates. — Avoid  side  plates  and  doubling  of  web 
plates. — Cheaper  to  use  heavy  flange  angles  in  stringers  rather  than  lighter 
angles  with  cover-plates. — Avoid  beveled  cuts. — Design  so  as  to  use  multiple 
punches. — -Do  not  crimp  stiffeners  for  ordinary  work. — Solid  web  versus 
lacing. — Avoid  hand-riveting. — Duplication  in  skew  spans. — Use  very  few 
sizes  of  pins  in  same  bridge. — In  riveted  tension  members  use  tie  plates 
instead  of  lacing. — ^AUow  ample  clearance. — When  metal  is  drilled  from  the 
solid  use  as  few  pieces  as  possible  in  make-up  of  sections. 
Mr.  Canady's  contribution  to  chapter:  Duplicate  spans. — Avoidance  of  light 
and  heavj^  trusses  in  same  span. — Long  panels. — Symmeliry. — Squaring 
small  skews. — -Treatment  of  skewed  spaiis. — Unnecessary  completeness  of 
many  engineers'  drawings. — Freedom  to  be  allowed  shops  in  rivet  spacing. — • 
Duties  of  shop  designing-engineer. — Full-punched  work. — Sub-punching. — •' 
Forge  and  machine-shop  work  to  be  a  minimum. — Curving  ends  of  girders. — 
Staggering  rivets. — Variety  of  rivet  diameters. — Web-plate  versus  lacing  for 
I-shaped  sections  of  struts. — -Thickening  of  stringer  webs. — Allowing  suffi- 
cient difference  between  gross  and  net  sectional  areas. — Fitting  of  fillers 
beneath  stiffeners. — -Avoiding  bevel  cuts. — ^Thickening  of  base  plates  to 
avoid  shop-work. — Coordination  of  different  parts  of  a  design 202 

CHAPTER  XXIV 

ECONOMICS   IN   DESIGN   FOR  ERECTION   CONSIDERATIONS 

Design  so  that  metal  will  go  together  easily  in  field. — Furnish  sufficient  clearance. — 
Wolf  el's  general  instructions. — Allow  one-half  inch  clearance  for  sheared 
ends. — Allow  for  "growth  of  steel." — Allow  ample  space  in  pockets. — Allow 
ample  width  for  packing. — Begin  erection  at  center  panel. — Arrange  for 
putting  floor  in  place  either  before  or  after  trusses  are  erected. — Detail 
through  plate-girders  so  as  to  avoid  spreading  them  in  field. — Half  pin-holes 
undesirable. — Entering  connections  to  be  avoided. — Clearance  for  packing.— 
Avoid  necessity  for  notching  timber  ties  to  clear  rivet-heads. — ^Minimize 
number  of  field  rivets. — Most  important  points  to  facilitate  and  cheapen 
erection. — Viaducts. — Make  two  bents  of  tower  alike. — Proper  lengths  for 
sections  of  columns. — Swinging-in  of  cross-frames 214 

CHAPTER  XXV 

ECONOMICS   OF   REINFORCED-CONCRETE   BRIDGES 

Economics  of  this  type  not  yet  so  highly  developed  as  that  of  older  types. — 
Intensity  of  stress  for  reinforcing  bars. — Objections  to  high-carbon  steel 
therefor. — Intensity  of  working  stress  for  concrete. — Pavings. — Hand  rails. — 
Designs. — Economics  of  design  rather  difficult  to  determine. — Slabs. — 
Girders. — Simple-span  girders  versus  continuous  girders. — Character  of 
foundations. — Balanced-cantilever  type  of  girder. — Columns. — Footings. — 


XVIU  CONTENTS 


Highway  girder-bridges. — Panel  length. — Girder  spacing. — Best  number  of 
columns  per  bent. — Economic  span-lengths. — Pile  foundations. — Arch 
bridges. — -Ratio  of  rise  to  span. — Abutment  reaction  affects  ratio  of  rise  to 
span. — Economic  span-length  with  rise  unchanged. — Factors  to  be  con- 
sidered.— Distance  from  springing  to  bottom  of  base. — Substructure  effects. 
— Massiveness  of  piers. — Ratio  of  live  load  to  dead  load. — Type  of  arch- 
ring. — Equality  or  inequality  of  adjacent  spans. — Arbitrary  requirements. — 
Other  special  conditions. — Solid  spandrel  versus  open-spandrel. — Solid 
barrel  versus  ribbed  structures. — Hingeless  and  three-hinged  arches. — Arch 
with  steel  bottom  chords. — Reinforced-concrete  trestles  for  steam-railways. — 
Slabs  therefor. — Special  economic  investigation. — Retaining  walls.        .      .     218 

CHAPTER  XXVI 

ECONOMICS  OF  STEEL  ARCH-BRIDGES 

Great  lack  of  reliable  information  thereon  prior  to  1918. — Failure  to  build  many 
steel  arch-bridges  in  America. — Author's  appeal  to  the  profession  for  inves- 
tigation on  arches.— Relation  between  metal  weights  in  arch  bridges  and 
corresponding  truss  bridges. — Paper  on  "Economics  of  Steel  Arch  Bridges" 
for  A.  S.  C.  E. — Invitation  to  discuss  same. — Effect  of  discussion. — Fowler's 
arch-dimension  compilation. — Economic  ratio  of  rise  to  span-length. — Eco- 
nomic rib-depths. — Percentage  effects  of  using  uneconomic  rib-depths. — 
Location  for  crown  hinge. — Solid-rib  versus  braced-rib  versus  spandrel-braced 
arches. — Three-hinged  versus  two-hinged  versus  hingeless  arches. — Com- 
bination of  three  hinges  for  dead  load  and  two  hinges  for  live  load. — Can- 
tilever arches. — Ratio  of  metal  weights  in  arch-bridges  and  corresponding 
truss-bridges. — Other 'economic  factors  than  weight  of  metal. — Side  issues 
of  investigation. — Percentage  equations  for  metal  weights  in  arches  and 
trusses. — Arches  more  economic  for  highway  than  for  railway  bridges. — 
Formulaj  for  weights  of  metal  in  arches  alone. — Limiting  span-length  for 
three-hinged  arches  of  carbon  steel. — Economic  or  practicable  limit  of  arch 
spans. — Influence  of  substructure  on  economics — Suitable  foundations  for 
arch  bridges. — Conclusion 232 

CHAPTER  XXVn 

ECONOMICS  OF  STEEL  TRESTLES,   VIADUCTS,   AND  ELEVATED 

RAILROADS 

Economic  factors  for  high  steel-railway-trestles. — Distance  from  center  to  center 
of  towers. — Modifications  necessary  for  three  diagrams  of  "Bridge  Engi- 
neering."— Economic  span-lengths  for  low  railway-trestles. — Double-track- 
railway  trestles. — Pedestal  costs  to  be  included. — Highway  trestles. — Column 
spacing  for  h(!nts  when  cantilevers  are  employed. — Elevated  railroads. — Best 
span  lengths  therefor. — Plate-girders  versus  open-webbed  girders. — Best 
sections  for  columns. — Paper  by  Mr.  Grcist 250 

CHAPTER  XXVni 

ECONOMICS   OF  CANTILEVER   BRIDGES 

Division  of  cantilevers  into  types. — Comparison  of  Types  A  and  B. — Comparison 
of  Types  A  and  C. — Comparison  of  Type  D  with  other  types. — Economic 


CONTENTS  XIX 

PAGE 

division  of  span-lengths. — Economic  truss  depths. — Legitimate  economies  in 
cantilever  designing. — Wind  stresses  during  erection. — Splaying  the  trusses. 
—Reducing  weight  during  erection. — Solitary  piers  or  pedestals  are  economic. 
— Adoption  of  intermediate  trusses. — Division  of  stress  on  members  meeting 
over  main  pier. — Choice  between  riveted  and  pin-connected  construction. — 
Box-section  chords. — Merriman  and  Jacoby's  treatment  of  cantilevers. — 
Truss-depth  constant  for  cantilevers:  the  practice  is  absurd. — Simple 
trusses  and  cantilevers  compared 257 

CHAPTER  XXIX 

ECONOMICS  OF  SUSPENSION   BRIDGES 

Much  still  to  be  learned  about  designing  suspension  bridges. — Suitable  mostly 
for  highway  structures. — Paper  on  "Comparative  Economics  of  Wire  Cables 
and  High- Alloy-Steel  Eye-bar-Cables  for  Long-Span  Suspension  Bridges." — ■ 
Best  floor  to  adopt. — Advantages  and  disadvantages  of  adopting  many 
lines  of  cables. — Economics  of  stiffening  trusses. — Best  panel  length. — 
Single-intersection  versus  double-intersection. — Ends  free  versus  ends 
anchored. — Versed  sine  of  cable. — Best  type  of  approaches. — Suspending 
floor  from  backstays. — Design  for  anchorages. — Economics  of  cables. — 
Unsuitability  of  suspension  bridges  for  steam  railways. — Effect  of  anchoring 
ends  of  trusses  upon  the  economics. — Comparative  advantages  and  disad- 
vantages of  two  types  of  cables. — Layout  for  proposed  suspension  bridge 
between  Philadelphia  and  Camden  and  description  of  structure. — Outline 
of  first  economic  investigation. — Live  loads  and  intensities  therefor. — 
Stress  theory  adopted  for  stiffening  trusses. — Second  set  of  computations. — 
Ratios  of  quantities  of  materials  in  eye-bar-cable  bridges  to  those  in  wire- 
cable  bridges. — Formulae  for  quantities  of  materials  in  suspension  bridges. — 
Diagrams  of  quantities  of  materials. — Unit  prices  of  materials. — Examples 
for  illustration. — Mayari  steel  comparison. — Heat-treated,  carbon-steel-eye- 
bar  comparison.  —  High-grade-nickel-steel  comparison.  —  Heat-treated, 
chrome-molybdenum-steel  comparison. — Resume  of  findings.        ....     263 

CHAPTER  XXX 

ECONOMICS   OF   MOVABLE  SPANS 

Types  considered. — Swing-span  versus  either  bascule  or  vertical  lift. — One  open- 
ing versus  two  openings. — Shifting  channel. — Vertical-lift  versus  bascule. — 
Future  raising  or  lowering  of  grade-line. — Skew-crossings. — Carrying  pipes 
and  wires  over  movable  spans. — Simplicity  of  vertical  lift. — Economics 
of  swing  spans. — Rim-bearing  versus  center-bearing  spans. — Bob-tailed 
swing  versus  ordinary  swing. — Economics  of  bascule  spans. — Single-leaf  bas- 
cule versus  double-leaf  bascule. — Double-leaf  bascule  unfit  for  railway 
bridges. — Heel  trunnion  bascule. — Thomas  Ellis  Brown,  Jr.,  type  of  bascule. 
— Rolling-lift  bascule. — Trunnion  type  of  bascule. — Waddell  and  Harring- 
ton axle  details.— Roller-bearing  type  of  bascule. — Brown-balance-beam  type 
versus  Strauss  type  of  bascule. — Economics  of  vertical-lift  spans. — Con- 
ditions favorable  to  the  vertical  lift. — Flanking  spans  for  vertical  lifts. — 
Skew  layouts. — Wind-pressure  on  movable  spans. — Widening  of  decks  of 
movable  spans. — Quickness  of  operation. — Economics  in  detailing  of  ver- 
tical lifts. — Best  material  for  counterweights. — Balancing-chains. — Buffers. 


XX  CONTENTS 


— Pavement  base. — Location  of  machinery  house. — Best  number  of  ropes. — 
Combination  of  vertical  Uft  and  cantilevers. — Design  for  Hoogly  Eiver 
Bridge,  Calcutta. — Comparative  costs  of  vario'is  types  of  movable  spans. — 
Records  of  quantities  of  materials  in  vertical-lift  and  bascule  bridges. — 
Percentage  weight-curves  for  vertical  lifts  and  bascules. — Housatonic  River 
Bascule  Bridge. — Unit  prices  used  in  comparison  of  total  costs. — Diagrams  of 
vertical  clearances  for  movable  spans  of  equal  cost. — Application  of  dia- 
grams to  skew  layouts. — Effect  of  substructure  conditions  on  comparative 
economics  of  vertical  lifts  and  bascules. — Comparative  costs  of  swing-span 
bridges  with  vertical  lifts  and  bascules. — Mystic  River,  Brown-Balance- 
Beam,  Bascule  Bridge. — Housatonic  River,  Bascule  Bridge. — General  ratio 
of  clear  height  to  clear  horizontal  opening  for  vertical-lift  bridges  and  bas- 
cules of  equal  cost. — Extension  of  investigation  for  economics  of  very  short 
spans  is  unnecessary,  and  why. 284 

CHAPTER  XXXT 

ECONOMICS  OF  OPERATING  MACHINERY  AND  POWER 

Data  furnished  by  Mr.  Thomas  E.  Brown  and  Major  Leon  L.  Clarke. — Kind  of 
power  and  type  of  machinery  depend  greatly  on  local  conditions. — Location 
near  a  city. — Steam  power  very  objectionable. — ^Hydraulic  pressure  or  com- 
pressed air. — Electric  power. — Internal-combustion-engine  power  and  its 
advantages. — Efficiency  definition. — Probable  time  of  operation. — Direct 
versus  alternating  current. — ^Accumulators. — Storage  batteries. — Hydraulic 
power. — ^Conveyance  of  power  on  span.  Gear  reduction. — Worm  gearing. — 
Multi-cylinder,  gasoline  engines  for  bridge  operation. — Ideal  apparatus. — 
Division  of  parts  of  movable  spans  into  three  groups. — Carrying  structure. — 
Supporting  machinery  parts. — Operating  machinery. — Breakdowns. — Power 
required  for  swings,  lifts,  and  bascules. — Amount  of  wind  pressure  for  bas- 
cule designing. — Brake  power  for  bascules. — Holding  power. — Economics 
in  using  standard  machinery. — Tendency  to  cramp  machinery  space.      .      .     310 

CHAPTER  XXXII 

POSSIBILITIES  AND  ECONOMICS  OF  THE  TRANSBORDEUR 

Various  names  for  this  type  of  structure. — ^Legitimate  function  of  transbordeur. — 
Transbordcur  versus  bridge. — Descrij^tion  of  transbordeur. — Author's 
development  of  tyi)e. — ^Types  of  bridge  suitable  for  supporting  transbordeur 
cages. — Transbordcur  design  for  New  Orleans. — Tabulation  of  (•onii)arativc 
costs  of  four  transhordeurs,  a  low-level  bridge,  nnd  a  high-level  bridge  for 
New  Orleans. — Deductions  from  table. — Comparative  economics  of  long 
cages  and  short  cages.— Best  number  of  cages  to  adopt. — Cost  of  operating 
transhordeurs. — Character  of  construction  and  general  modus  operarnii  of 
transbordeur. — Details  of  structure. — Operation  of  New  Orleans  trans- 
bordeur.— Conditions  necessitating  a  "corral." — Method  of  caring  for 
ped(!strians. — -Time  sdjedules. — Evolution  of  author's  transbordeur  type. — 
C'()m()arison  of  cai)a('iti(^s  of  transl)ordeur  and  low-level  bridge. — O])])ortuiii- 
tioH  for  buihhiig  transhordeurs  are  S(Uirce. — Fixed-span  bridge  iircferablc  (o 
traiisbordeur. — 'I'nuisbonk'ur  design  for  Havana  Harbor. — Phila(l('li)liia- 
Carnden  transbordeur  design. — Cotidusion  and  recapitulation.        .  .     318 


CONTENTS  XXI 

CHAPTER  XXXIII 
ECONOMICS  IN   CONTRACT-LETTING 

PAGE 

Proper  contract  letting  is  a  matter  of  real  economics. — Author's  discussion  of 
paper  by  Mr.  Ernest  Wilder  Clarke. — Importance  of  subject. — Business 
opportunity  of  the  U.  S.  A. — Prevention  of  progress. — Labor  and  capital. — 
Men  who  do  the  work  must  share  in  the  profits,  but  preferably  not  in  the 
management  of  business. — Quieting  popular  unrest. — Various  methods  of 
contract  letting  listed. — Description  of  each  method. — Injustice  of  straight- 
lump-sum  contracts. — Advantages  of  unit-price  method. — Cost-plus  method. 
— Hospital  jobs. — Conscientiousness  of  contractors  and  workmen. — ^Paying 
by  the  job. — Cost-plus  methods  cut  out  competition. — All  ordinary  methods 
are  faulty. — Salient  features  of  an  ideal  system. — Description  of  the  ideal 
method. — -Method  of  profit-sharing  contract. — Application  of  corrective 
ratio. — Employee's  percentage  of  total  profits. — Method  of  anticipating  rise 
or  fall  of  prices. — Exemplification  of  ideal  method. — ^Advantages  of  ideal 
method. — Objections  that  have  been  raised  thereto. — Adoption  of  method. — 
Addendum  re  profit-sharing  in  manufactories.  ..,..,...     337 


CHAPTER  XXXIV 

ECONOMICS  OF  BRIDGE-ENGINEERING  OFFICEWORK 

Scheme  of  management  expounded  in  Chapter  LVIII  of  "Bridge  Engineering." — • 
General  principles  for  office  management. — Employees  should  reach  office  on 
time. — No  talking  in  office. — No  visitors  should  be  allowed  in  office. — No 
smoking  in  office. — Employees  should  attend  strictly  to  their  own  business. — • 
Collecting  full  data  before  starting  computations. — Limits  of  accuracy  in  cal- 
culations.— ^Checking  calculations. — Filing  and  indexing. — Drawings. — ■ 
Standards. — Lettering. — No  issuing  of  unchecked  drawings. — Blank  forms. 
—Cost  records. — Card  indices 358 

CHAPTER  XXXV 

ECONOMICS   OF  INSPECTION 

Subject  somewhat  intangible. — To  what  extent  will  it  pay  owner  to  inspect? — ■ 
Compensation  for  inspection. — Quality  of  inspection. — Methods  of  pay- 
ment for  inspection. — Omission  of  inspection. — Supervision  by  direct  employ- 
ees of  the  Engineer. — Inspection  by  established  bureaus. — Economy  in  per- 
formance.— Start  shop  inspection  at  beginning  of  work. — Ground  to  be 
covered  by  shop  inspection. — Economics  of  mental  effort  for  shop  inspectors. 
—Field  inspection. — General  question  of  the  Economics  of  Inspection.        .     361 

CHAPTER  XXXVI 

ECONOMICS  OF  SHOPWORK 

Necessity  for  aid  of  shop  expert  in  preparing  notes  for  this  chapter. — Importance  of 
systemization   of   one's   knowledge. — Assistance   of   Mr.    Earle. — General 


XXU  CONTENTS 

PAGE 

economic  problem  stated. — Design  of  shop  for  special  class  of  work  or  for 
general  work. — Keeping  shop  force  occupied. — Transportation  of  materials 
in  shop. — Principal  economic  factors  in  shopwork. — Scrapping  tools  and 
apparatus  for  betterment. — Light. — Interior  painting  of  shop. — Heat. — 
Ventilation. — Space. — Handling  of  work. — Management  of  men. — Safety 
considerations  and  their  importance. — Prevention  of  accidents  and  how  to 
accomplish  it. — Smoking  on  premises. — Anticipating  troubles. — Standardi- 
zation.— Stock  materials  and  storing  thereof. — Supply  of  labor. — Tool  equip- 
ment.— Shop  floors. — Straightening  metal. — Marking  metal. — Trimming 
and  cutting. — Punching. — Drilling. — Storage  of  punched  metal. — Assem- 
bUng. — Reaming. — Riveting. — MUling  and  planing. — Boring. — Special 
space. — Machine  shop. — Foimdry. — Blacksmith  shop. — Match  marking. — 
Painting. — Tracks. — Templet  shop. — Recapitulation 365 


CHAPTER  XXXVII 
ECONOMICS  OF  BRIDGE-ENGINEERING  FIELDWORK 

Instructions  to  Resident  Engineer. — Starting  work  ahead  of  contractor. — Employ- 
ing smallest  force  consistent  with  efficiency. — Keeping  force  busy. — Laying 
out  on  paper  an  economic  system  for  carrying  on  fieldwork. — Prevention  of 
dropping  behind  on  work — Supplying  home  office  with  information. — Testing 
cement. — Checking  receipt  of  materials. — Unloading  materials  quickly. — 
Aiding  contractor. — Prompt  monthly  estimates. — Extras. — Progress  reports. 
— Resident  Engineer  is  a  confidential  agent  and  not  a  principal. — Insuring 
field  property. — Copying  survey  notes. — Diary. — Resident  Engineer  must 
act  in  a  semi-judicial  capacity. — Care  of  instrimaents. — Non-abuse  of  power. 
— Storing  materials. — No  damage  to  reinforcing  bars. — Care  of  paving 
blocks. — Protecting  cement  against  weather. — Care  of  explosives. — 
Falsework  and  forms. — Sinking  cribs  and  caissons. — Building  up  cribs  and 
caissons. — Depositing   concrete   under   water 380 

CHAPTER  XXXVIII 

ECONOMICS    OF    BRIDGE-CONTRACTOR'S    GENERAL    FIELDWORK 

Data  furnished  by  Mr.  H.  K.  Seltzer. — Contractor's  guiding  principle  in  perform- 
ance of  work. — List  of  main  subjects  requiring  Contractor's  attention  at 
outset. — Field  organization. — Plant. — Yards,  wharves,  and  tracks. — Plans 
of  buildings  and  plant. — Materials  and  supplies. — General  notes.       .     .     .     383 

CHAPTER  XXXIX 

ECONOMICS  OF   CONCRETE   MIXING 

Two  main  points  of  view  for  consideration  of  problem. — Contractor's  viewpoint. — 
Duty  of  the  Engineer. — How  to  j)r()ducc  strongest  concrete. — Legitimate 
major  ways  for  a  contractor  to  economize  in  concrete-mixing. — Minor  ways 
for  economizing. — List  of  economic  problems. — Best  proportions  of  materials. 
— Reduction  of  voids  in  the  aggregate. — Using  a  mixture  of  gravel  and  sand 
without    screening. — Water-proofing. — Increasing    fluidity    of    mixture. — 


CONTENTS  Xxiii 

PAQE 

Manner  and  time  of  mixing. — Using  of  large  stones  in  mass. — ^Vibration  and 
jigging  of  freshly-made  concrete. — Age  of  cment. — Protection  of  fresh 
concrete. — General  remarks. — Indebtedness  for  suggestions  to  Mr.  J.  J. 
Yates 386 

CHAPTER  XL 

ECONOMICS   OF  ERECTION 

Indebtedness  for  data  to  Mr.  Frank  W.  Skinner. — Bridge  erection  is  a  function 
of  design,  location,  and  available  equipment. — Specialization  of  bridge 
erection. — Division  of  subject. — Steel  bridges. — Completion  of  fabrication 
at  bridge  shops. — Use  of  standard  plant  and  equipment. — Skilful  and 
experienced  labor  necessary. — Complication  of  problem  by  artificial  condi- 
tions.— Girder  spans. — Limits  in  dimensions. — Derrick  cars,  derricks,  gin- 
poles,  and  other  erection  apparatus. — Viaduct  erection. — Ideal  method  is  by 
derrick  traveler  or  mule. — Cantilever  travelers. — Strident  gantry  traveler. — 
Medium  spans. — Pile  foundations. — Supplementary  gantry  traveler. — 
Alternative  methods. — Cantilever  erection. — Erection  on  eccentric  false- 
work.— Method  of  protrusion. — Erection  on  moving  suspending  platform. — 
Distribution  of  steel  on  ground. — rMethod  of  flotation.- — Erection  from  tem- 
porary suspension  span. — Long  spans. — Framed-timber  falsework. — Canti- 
lever method. — Limiting  lengths  for  cantilever  spans. — Assisted  cantilever 
method  of  erection. — Erection  of  suspended  spans  by  flotation  and  hoisting. 
— Suspension  bridges. — Methods  of  erection. — Arch  spans. — Methods  of 
erection. — Cantilevering  arches. — Erection  plant.— Steel  travelers. — Struc- 
tural-steel falsework. — Yokes,  clamps,  etc. — Replacing  steel  bridges. — Main- 
tenance of  traffic. — Diversion  of  traffic. — Replacing  short  spans  on  old  sub- 
.:jtructure. — Use  of  barges  therefor. — Replacing  by  transverse  displacement. 
—Replacing  long  spans. — Erection  of  concrete-girder  bridges  and  concrete- 
arch  spans 396 

CHAPTER  XLI 

ECONOMICS  OF  MAINTENANCE^  AND  REPAIRS 

Data  furnished  for  chapter. — Old  rule  of  author's  for- passing  upon  over-stressed 
structures. — Converting  two  old  bridges  into  one. — Repairing  bridges  that 
should  be  relegated  to  the  discard. — Criterion  for  determining  whether  to 
repair  or  to  discard. — But  little  repair  work  now  done  by  consulting  engi- 
neers.— Mr.  Loweth's  letter  and  contribution. — Shifting  light  structures  to 
branch  lines. — Necessity  in  war  times  for  repairing  structures  thai  at  other 
times  would  have  been  removed. — "Carrying  Bridges  Over." — Shifting 
overloaded  bridges  to  branch  lines. — Strengthening  bridges  in  place. — 
Example  of  problem  in  repairing  or  replacing. — General  considerations. — 
Classification  of  bridges. — Determination  of  safe  unit  stresses  for  actual 
maximum  loading. — List  of  factors  affecting  such  determination. — Standard 
loadings. — General  method  of  investigating  a  bridge. — Classification  of  load- 
ings.— Speed  restrictions. — Where  low  classification  usually  occurs  in  bridges. 
— Timber  trestles. — Safe  unit  stresses  for  timber. — Effect  of  brine  drippings. 
— Effect  of  locomotive  smoke. — Fatigue  of  metal  in  bridges  is  a  fallacy. — 
Strengthening  of  light  steel  bridges. — Strengthening  timber  bridges. — 
Strengthening  versus  renewal  and  examples  thereof. — Conditions  shaping  the 
general  policy  concerning  the  keeping  of  light  bridges  in  service. 


XXIV  CONTENTS 

PAGE 

Mr.  Heritage's  contribution  to  this  chapter:  Definition  of  most  economical 
structure. — Periodical  inspection. — Inspection  departments. — Repairs  to 
timber  bridges  and  pile-driven  trestles. — Tools  for  bridge-repairing  gangs. — 
Preservation  of  timber. — Fire- protection. — Planks  no  longer  fit  for  highway 
bridge-floors. — Old  masonry  piers  and  abutments. — Repointing. — Concrete 
piers. — Steel  cylinder  piers. — Protection  against  corrosion  of  steel. — Paint 
and  painting. — Cleaning  of  metalwork. — Application  of  paint. — Spraying 
of  paint. — Signs  of  deterioration  in  connections. — Wear  on  pins. — Wear  at 
intersection  of  diagonals. — Overstress  on  counters. — Joint  contribution  of 
Mr.  Chalfant  and  Mr.  Covell. — Division  of  subject. — Masonry. — Scouring  . 
of  bed  and  cutting  of  banks. — Turning  of  stream. — Rip-rapping. — System- 
atic soundings. — Floors. — Best  type  of  pavement  and  base. — Concrete 
slab. — Buckle-plate  floors. — Plank  floors  are  antiquated. — Weight  of  trucks 
too  great  for  timber  floors. — Nailing-pieces  for  stringers. — Stringer-spacing. 
— Laying  of  planks. — RaU  supporting. — Laying  of  wood-blocks. — Hillside 
blocks. — Crowning  of  roadway. — Sidewalks. — Adjusting  old  back-wall  to 
new  grade. — Replacing  of  floors. — Itemized  record  of  repairs. — Detection  of 
decay  in  timber. — Painting. — Division  of  territory  for  painting. — Colors  for 
bridge  paints. — Cleaning  and  repainting  of  metal  below  flooring. — Paint 
formulae 407 

CHAPTER  XLII 

ECONOMICS  OF   METAL  PROTECTION 

Importance  of  proper  protection  of  metalwork. — Duration  of  life  of  metallic 
structures. — Subjects  included  in  the  economics  of  metal  protection. — Best 
kinds  of  paint  for  shop  and  field. — Author's  experience  with  paints. — Ideal 
paint  for  shop  coat. — Finishing  coats. — Havre  de  Grace  test  of  paints. — 
Houston  Lowe's  conclusions  concerning  the  characteristics  of  good  bridge 
paints. — Objections  to  the  old-fashioned,  red-lead  paints. — Amount  of  red- 
lead  pigment  per  gallon  of  vehicle. — Varying  elasticity  of  paint  coats. — 
Functions  of  an  anti-corrosive  metal-coating. — Best  vehicle  for  paint. — 
Author's  experiments  on  paints  in  Mexico. — Use  of  driers. — Best  colors  for 
paints. — Covering  and  spreading  powers  of  paints. — Cement  paints. — Lin- 
seed oil  alone  for  shop  coat. — Climatic  influences  on  paints. — Salt-water-proof 
paint. — A  special  paint  for  the  hot  climate  of  Brazil. — Spraying  of  paint. — 
Spraying  on  metalwork  for"  shop  coat. — Cleansing  paint. — Pickling. — Paint- 
ing newly-erected  steelwork. — Concrete  encasement. — Gunite. — Treat- 
ment of  st^el  that  has  to  be  encased  in  concrete  or  gunite. — Protection 
against  brine  drippings. — Protection  against  locomotive  gases. — Causes  of 
paint  deterioration. — How  to  care  for  incipient  failure  of  paint. — Deter- 
mination of  time  for  repainting. — Cleansing  of  metalwork  preparatory  to 
apf)lying  now  field  coats. — Application  of  paint  after  cleaning. — Factors  that 
affect  resulls  in  painting. — E(!onomic  observations  concerning  jxiinting  in 
general. — Price  of  paint. — Thickness  of  coats. — Character  ,of  brush. — 
liest  temperature  for  paintingf — Special  kinds  of  paint  for  special  conditions. 
— Summary 430 

CHAPTER  XLIII 

ECONOMICS   OF   WATER-PROOFING 

Aid  from  Mr.  J.  B.  W.  Gardiner. — Definition  of  cc^ononiics  of  water-])roofing. — 
Profitablen(!SS  of  wat(!r-{)ro()fing. — Factors  affecting  cost  of  water-|)r()ofiiig. — 


CONTENTS  XXV 


Relative  cost  of  water-proofing  to  that  of  total  cost  of  structure. — Interest 
on  investment  may  be  ignored.— Probable  life  of  water-proofing. — Qual- 
ities of  materials  for  water-proofing. — Deterioration  of  water-proofing  and 
causes  therefor. — Damage  due  to  lack  of  water-proofing. — Water-proofing 
in  steel  bridges. — Brine  drip. — Water-proofing  of  concrete  viaducts. — 
Water-proofing  of  flat  slabs. — Water-proofing  of  concrete  roads. — Disin- 
tegrating effects  of  water-penetration  on  concrete. — Leaching  of  alkalies. — 
Erosive  action  of  water  percolating  concrete. — Effect  of  freezing  on  rein- 
forced concrete. — Cracks  in  floor  slabs. — Electrolysis. — -Softening  of  con- 
crete and  expansion  thus  induced. — Appearance  deteriorated  by  water  per- 
colation.— Excrescence  of  magnesia  and  other  salts. — .Esthetics  and  eco- 
nomics.— Water-proofing  is  a  form  of  insurance. — ^Effect  of  this  disserta- 
tion on  author's  future  policy  in  the  designing  and  construction  of  bridges. — 
Mr.  Rhett's  conclusions  re  water-proofing 449 


CHAPTER  XLIV 

ECONOMICS  OF   MILITARY   BRIDGES 

Fundamental  Economics  of  Military  Engineering. — Time  factor  substituted  for 
cost  factor. — Principle  of  "Bare  Necessities  Only." — Safety  and  perma- 
nence.— Waste  not  justifiable. — Classes  of  Military  Bridges. — -Types  of 
Military  Bridges. — -The  typical  military  bridge. — Framed  trestles. — 
Economic  span  for  military  trestle  bridges. — ^Spar  bridges. — Pile  trestles. — 
Trusses. — Sectional  trusses  and  girders. — Cribs. — Suspension  bridges. — 
Ponton  or  floating  bridges. — New  type  of  ponton  equipage. — Raflroad 
bridges. — Foot-bridges. — -Deck  or  flooring  of  military  bridges. — Width  of 
roadway. — Side-rails  and  hand-rails.—  Materials  employed  in  Military 
Bridging.  —  Timber.  —  Piling.  —  Steel.  — ■  Concrete.  —  Stone.  —  Paint.  — 
Joints  and  fastenings. — Sizes  of  individual  members. — Plant  and  tools. — 
Class  of  labor  available. — Improvisation  and  standardization. — Utilization  of 
existing  bridges. — Utilization  of  Iccal  resources. — -Loading  of  military 
bridges. — -Transportation  of  materials. — Selection  of  site. — Protection 
against  flood  and  drift. — Inspection  of  mflitary  bridges 459 

CHAPTER  XLV 

CONCLUSION 

Explanation  of  innovation  in  technical  literature. — Reasons  why  this  is  to  be 
author's  last  technical  treatise. — Great  expense  involved  in  technical-book 
writing. — Great  amount  of  valuable  time  involved. — Subject  of  bridges 
about  exhausted  by  author's  various  writings. — Probable  economic  investi- 
gation on  "Molybdenum  Steel  for  Bridges." — This  treatise  is  mainly 
author's  own  personal  work. — Suggested  method  of  utilizing  "Bridge 
Engineering  "  and  "Economics  of  Bridgework  "  by  young  engineers  desirous 
of  becoming  "Bridge  Experts." 486 

APPENDIX 

Chronologically  arranged  list  of  author's  various  investigations  and  writings  on  the 

subject  of  "Bridge  Economics." 489 


LIST  OF  ILLUSTRATIONS 


CHAPTER  V 
ECONOMICS   OF  ALLOY  STEELS 

PAGE 

Fig.    5a.     Economic    Limiting-Values   of   rr'   for     Simple-Span,    Steam-Railway 

Bridges 28 

Fig.    56.     Economic    Limiting-Values    of    rr'    for    Cantilever,    Steam-Railway 

Bridges 29 

Fig.  5c.  Total  Weights  of  Metal  per  Lineal  Foot  of  Span  for  Double-Track, 
Steam-Railway,  Cantilever  Bridges  of  Carbon  Steel  and  Alloy-Steels 
of  Various  Elastic  Limits 31 

Fig.  5d.  Diagram  Showing  Comparative  Economics  of  All  Procurable,  or  Prac- 
tically-Possible, High-Alloy  Steels  for  Long-Span,  Cantilever  Bridges       32 

CHAPTER  VI 

COMPARATIVE   ECONOMICS   OF   BRIDGES   AND   TUNNELS 

Fig.  6a.  Diagram  of  Total  Costs  of  Highway  and  Electric-Railway  Bridges 
and  Tunnels,  with  their  Approaches,  for  Crossings  Similar  to  that  of 
the  North  River  at  New  York  City 58 

CHAPTER  XI 

COMPARATIVE  ECONOMICS  OF  CONTINUOUS  AND  NON- 
CONTINUOUS  TRUSSES 

Fig.  11a.  Layout  of  Petit-Truss,  Continuous  Spans 76 

Fig.  116.  liayout  of  Petit-Truss,  Non-Continuous  Spans 76 

Fig.  lie.  Layout  of  Subdivided-Triangular-Truss,  Continuous  Spans        ...  79 

Fig.  lid.  Layout  of  Subdivided-Triangular-Truss,  Non-Continuous  Spans     ,      .  79 

CHAPTER  XII 

COMPARATIVE  ECONOMICS  OF  SIMPLE-TRUSS  AND 
CANTILEVER  BRIDGES 

Fig.  12a.  Typical  Layouts  for  Double-Track-Railway,  Cantilever  Bridges  .  85 
Fig.  126.     Comparative    Weights    of    Metal    for    Double-Track,    Simple-Truss 

Bridges  and  Type-C-Cantilever  Bridges 86 

Fig.  12c.     Comparative    Weights    of    Metal    for    Double-Track,    Simple-Truss 

Bridges  and  Type-A-Cantilever  Bridges 87 

xxvii 


XXVm  LIST  OF   ILLUSTRATIONS 

CHAPTER  XIII 

COMPARATIVE  ECONOMICS  OF  CANTILEVER  AND 
SUSPENSION  BRIDGES 


PAGE 

95 
95 
96 
97 


Fig.  13a.  Layout  for  1,700-root-Span,  Cantilever,  Railway  Bridge 

Fig.  136.  Layout  for  1,700-Foot-Span,  Suspension,  Railway  Bridge 

Fig.  13c.  Cost-Curves  for  Double-Track-Railway  Bridges    .      . 

Fig.  13d.  Layout  for  2,400-Foot-Span,  Cantilever,  Railway  Bridge 

Fig.  13e.  Layout  for  2,400-Foot-Span,  Suspension,  Raih\'ay  Bridge 

Fig.  13/.  Modified  Cost-Curves  for  Double-Track-Railway  Bridges     ....       99 

Fig.  13^.  Dr.  Steinman's  Layouts  for  Cantilever  Bridges 101 

Fig.  13/i.  Dr.  Steinman's  Layouts  for  Suspension  Bridges    .            .    ' .      .      .      .     101 
Fig.  ISi.  Cost-Curves  for  Combined  Railway  and  Highway  Bridges  ot  the  Gen- 
eral Type  Computed  by  Dr.  Steinman 105 

Fig.  13/.  Cost-Curves  for  Highway  Bridges  of  Carbon  Steel 107 

Fig.  ISJfc.  Diagram  of  Main-Span  Lengths  of  Equal  Cost  for  Combined-Railway- 

and-Highway,  Cantilever  and  Suspension  Bridges      .      .      .      .      .      .      109 

CHAPTER    XVII 

ECONOMICS  OF  TIME  AND   MONEY  IN   MAKING  COST- 
ESTIMATES  FOR  BRIDGES 

Fig.  17o.  Profile  for  Student  Problem  No.  1 148 

Fig.  176.  Profile  for  Student  Problem  No.  2 148 

Fig.  17c.  Profile  for  Student  Problem  No.  3 148 

Fig.  17d.  Profile  for  Student  Problem  No.  4    . .  148 

1 

CHAPTER  XVIII 

ECONOMIC  SPAN-LENGTHS  FOB  SIMPLE-TRUSS  BRIDGES  ON 
VARIOUS  TYPES   OF   FOUNDATION 

Fig.  18a.     Live-Plus-Impact  Loads 153 

Fig.  186.     Live  Loads  without  Impact         154 

Fig.  18c.     Total  Weights  of  Metal  in  Superstructures 155 

Fig.  18f/.     Costs  per  Lineal  Foot  of  Structure  for  Low-Level,  Combined  Bridges 

on  Sand  Foundations  100  Feet  Deep 159 

Fig.  18e.     Costs  per  Lineal  Foot  of  Structure  for  Low-Level,  Combined  Bridges 

on  Sand  Foundations  150  Feet  Deep 101 

Fig.  18/.      Costs  per  Lineal  Foot  of  Structure  for  Low-Level,  Combined  Bridges 

on  Sand  Foundations  200  Feet  Deep 162 

Fig.  18f/.     Costs  per  Lineal  Foot  of  Structure  for  Low-Level,  Combined  Bridges 

on  Sand  Foundations  2.50  Feet  Deep Ili3 

Fig.  18/i.     Economic  Span-Lengths  for  Simple-Truss  Bridges  on  ^'ari<nls  Ty])es  of 

Foundation Itil 

Fig.  ISt.      Diagram  of  Weight-Ratios  showing  Effect  of  Lengthening  the  ('entral 

Span  of  any  Simple-Truss,  Three-Span  Layout,  Keeping  the  Total 

Length  Unchanged 100 

CHAPTER  XX 

ECONOMICS   OF   TRUSSES    AND    GIRDERS 
Fig.  20o.     Economic  Depths  of  Plate-Girders  with  Riveted  End-Connections   .      .      180 


LIST  OF   ILLUSTRATIONS  XXIX 

CHAPTER  XXI 
ECONOMICS   OF   DECKS  AND   FLOOR  SYSTEMS 

PAGE 

Fig.  21a.     Diagram  of  Increase  in  Weight  of  Metal  for  Each  Excess  Pound  of 

Extraneous,  Uniformly-Distributed  Load  in  Simple-Truss  Spans   .      .      196 

Fig.  216.     Diagram  of  Increase  in  Weight  of  Metal  for  Each  Excess  Pound  of 
Extraneous,     Uniformly-Distributed     Load     in     Type-A-Cantilever 
Bridges 197 

CHAPTER  XXIV 

ECONOMICS   IN   DESIGN   FOR   ERECTION   CONSIDERATIONS 

Fig.  24a.     Trough-Floor  Construction  for  Easy  Field-Riveting 214 

CHAPTER  XXVI 

ECONOMICS   OF   STEEL   ARCH-BRIDGES 

Economic  Ratios  of  Depth  of  Arch-Rib  to  Span  Length       ....     236 
Effects    on    Rib-Weights    from    Using    Uneconomic   Rib-Depths    in 

Braced-Rib  Arches 236 

Ratio  of  Weights    of  Metal    in  Hingeless  Arches  as  Compared  with 
Three-Hinged  Arches  for  both  Railway  and  Highway  Bridges   .      .      .     237 
Percentages  to  Apply  to  Weights  of  Metal  in  Trusses  of  Simple-Truss 
Spans  in  Order  to  Find  the  Weights  for  Arch-Ribs  and  the  Superim- 
posed Columns,  with  their  Bracing,  to  Carry  the  Same  Live  Loads   .      .      238 
Weights  of  Metal  in  Double-Track,  Steam-Railway,  Long-Span  Arch- 
Bridges  of  Carbon  Steel  for  Class-60  Live-Load 241 

Economics  of  Solid-Rib  Arches,  with  Columns  and  Bracing,  for  Steam- 
Railway  Structures,  in  Relation  to  Ratios  of  Rise  to  Span-Length   .      .      242 
Economics  of  Solid-Rib  Arches  for  Steam-Railway  Structures  (Ribs 
Alone  Considered),  in  Relation  to  Ratios  of  Rise  to  Span-Length   .      .      243 
Economics   of   Braced-Rib   Arches,   with   Columns  and   Bracing,   for 
Steam-Railway  Structures,  in  Relation  to  Ratios  of  Rise  to  Span-Length     244 
Economics  of  Braced-Rib  Arches  for  Steam-Railway  Structures  (Ribs 
Alone  Considered),  in  Relation  to  Ratios  of  Rise  to  Span-Length   .      .      245 
Canadian  Northern  Pacific  Railway  Bridge  over  the  Eraser  River  at 

Lytton,  B.  C.        . 246 

Arch  Bridge  over  the  Waikato  River  at  Hamilton,  N.  Z 246 

Arch  Bridge  over  the  Waikato  River  at  Cambridge,  N.  Z 247 

Arroyo  Seco  Bridge  at  Pasadena,  Calif 248 

Colorado  River  Bridge  at  Austin,  Texas 249 

CHAPTER  XX  711 

ECONOMICS  OF  STEEL  TRESTLES,  VIADUCTS,  AND  ELEVATED 

RAILROADS 

Fig.  27a.     Economic  Span-Lengths  for  High,  Single-Track-Railway  Trestles   .      .      251 
Fig.  276.     Economic  Span-Lengths  for  Low,  Single-Track-Railway  Trestles   .      .     252 


Fig. 

26a. 

Fig. 

266. 

Fig. 

26c. 

Fig. 

2M. 

Fig. 

26e. 

Fig.  26/. 

Fig. 

26^. 

Fig. 

26A. 

Fig. 

26i. 

Fig. 

2Qj. 

Fig. 

2Qk. 

Fig. 

261. 

Fig. 

26m. 

Fig. 

26n. 

XXX  LIST   OF   ILLUSTRATIONS 

CHAPTER  XXIX 

ECONOMICS  OF  SUSPENSION  BRIDGES 

PAGE 

Fig.  29a.     Layout  of  Wire-Cable -Suspension-Bridge 271 

Fig.  296.     Layout  of  Eye-bar-Cable  Suspension-Bridge 271 

Fig.  29c.     Quantities  for  Wire-Cable  Suspension-Bridges 276 

Fig.  29d.  Weights  of  Alloy-Steel  Eye-bars  in  Eye-bar-Cable  Suspension-Bridges   .  277 

Fig.  29e.  Quantities  of  Various  Materials  in  Eye-bar-Cable  Suspension  Bridges  .  278 

CHAPTER  XXX 

ECONOMICS   OF   MOVABLE   SPANS 

Fig.  30a.  Layout  for  Proposed  Hoogly  River  Bridge  at  Calcutta,  India  .  .  .  296 
Fig.  306.     Percentage  Weights  for  Double-Track-Railway,  Vertical-Lift  Bridges 

and  Single-Leaf,  Heel-Trunnion  Bascules 299 

Fig.  30c.     Layouts  with  No  Flanking  Truss-Spans 300 

Fig.  30d.     Layouts  with  Flanking  Truss-Spans 300 

Fig.  30e.     Comparative  Costs  of  Double-Track-Railway,    Vertical-Lift    Bridges 

and  Single-Leaf,  Heel-Trunnion  Bascules 302 

Fig.  30/.  Clear  Channels  and  Clear  Heights  for  Equal  Costs  of  Double-Track- 
Railway,  Vertical-Lift  Bridges  and  Single-Leaf,  Heel-Trunnion  Bas- 
cules        303 

Fig,  30</.     Layouts  with  Flanking  Truss-Spans — Bascule  Tower  Cantilevered       .     304 

CHAPTER  XXXII 
POSSIBILITIES   AND   ECONOMICS   OF   THE   TRANSBORDEUR 

Fig.  32a.     Layout  of  Proposed  Transbordeur  for  Crossing  the  Mississippi  River 

at  New  Orleans,  La 322 

Fig.  326.  Second  Preliminary  Study  for  Proposed  New  Orleans  Transbordeur  .  326 
Fig.  32c.  Third  Preliminary  Study  for  Proposed  New  Orleans  Transbordeur  .  329 
Fig.  32d.     Fourth  Preliminary  Study  for  Proposed  New  Orleans  Transbordeur  329 

Fig.  32e.     Ratios  of  Costs  of  Fixed-Span  Bridges  and  their  Approaches  for  Various 

Clearances  above  High  Water    .      .      . 331 

Fig.  32/.     Proposed  Bridge  across  the  Entrance  Channel  to  the  Harbor  of  Havana, 

Cuba 333 

Fig.  32^.     General  Layout  for  a  Proposed  Transbordeur  to  Cross  Havana  Harbor, 

Cuba 334 

CHAPTER  XXXIII 

ECONOMICS   OF   CONTRACT  LETTING 

Fig.  33a.     Total  Percentage  of  Saving  on  Limiting  Cost  to  Client 346 

Fig.  336.     Diagram  of  Corrective  Ratios 347 

CHAPTER  Xi.1 

ECONOMICS   OF   MAINTENANCE   AND   REPAIRS 

Fig.  41a.     Diagram    Showing    Classification    of    U.   S.   Government.    Standard 

[jocoinotives 413 

Fig.  416.     Diagram  Showing  Classification  of  Typical  Loailings 413 


LIST  OF  TABLES 


CHAPTER  IV 

EFFECT  ON  ECONOMICS  FROM  VARIATIONS  IN  MARKET  PRICES 
LABOR  AND    MATERIALS 


OF 


PAGE 


Table    4a.     Economic  Span-Lengths  for  Double-Track,  Steam-Railway  Bridges 
on  Sand  Foundations  at  Various  Depths  below  Extreme  Lo  w- Water 


24 


Table 

5a. 

Table 

5b. 

Table 

5c. 

Table 

5d. 

Table 

5e. 

Table 

5/. 

Table 

5g. 

Table 

5h. 

Table 

m. 

Table 

5.7. 

Table 

5k. 

Table 

51. 

Table 

5m, 

CHAPTER  V 

ECONOMICS  OF  ALLOY  STEELS 

Heat-Treated  Chrome  Steel  with  and  without  Molybdenum     .     .  38 

Tensile  Test  on  Chromol  Steel 38 

Tensile  and  Dynamic  Tests  on  Nichro  Steel      .......  39 

Tensile  and  Dynamic  Tests  on  Nichromol  Steel 39 

Tensile  Tests  on  Chrovan  Steel 40 

Tensile  Tests  on  Chrovanmol  Steel 40 

Tensile  Tests  on  Nickel  Steel  . 41 

Tensile  Tests  on  Nicmol  Steel 41 

Tensile  Tests  on  Carmol  Steel,  No.  1 42 

Tensile  Tests  on  Carmol  Steel,  No.  2 42 

Tensile  Tests  on  Chromol  Steel  (Untreated) 43 

Tensile  Tests  on  Chromol  Steel  (Treated) 43 

Resume  of  Findings  and  Deductions 61 


CHAPTER  XI 

COMPARATIVE  ECONOMICS  OF  CONTINUOUS  AND  NON- 
CONTINUOUS  TRUSSES 

Table  11a.     Summary  of  Weight  Ratios — Divided  Triangular  Trussing    . 
Table  116.     Summary  of  Weight  Ratios — Petit  or  Pratt  Trussing  .... 


80 

81 


CHAPTER  XIII 

COMPARATIVE  ECONOMICS  OF  CANTILEVER  AND  SUSPENSION 

BRIDGES 

Table  13a.     Dr.  Steinman's  Weights  of  Metal .     .     .     .     103 

Table  13&.     Comparison  of  Substructure  Costs     .      ..,.     .' 104 


XXXU  LIST   OF   TABLES 


CHAPTER  XVIII 

ECONOMIC  SPAN-LENGTHS  FOR  SIMPLE-TRUSS  BRIDGES  ON 
VARIOUS  TYPES  OF  FOUNDATION 

PAGE 

Table  18a.     Weights  of  Flooring  per  Lineal  Foot .     .  > 156 

Table  186.     Unit  Prices  of  Materials  in  Place 156 

Table  18c.     Resume  of  Results  of  Computations 160 


CHAPTER  XXrX 

ECONOMICS  OF  SUSPENSION  BRIDGES 

Table  29a.    Ratios  of  Quantities  of  Materials  in  Eye-bar-Cable  Bridges  to  those 

in  Wire-Cable  Bridges 273 

CHAPTER  XXXII 

POSSIBILITIES  AND   ECONOMICS  OF  THE  TRANSBORDEUR 

Table  32a.     Estimated  Costs  of  Various  Proposed  Structures  for  Crossing  the 

Mississippi  River  at  New  Orleans 320 

CHAPTER  XXXIX 

ECONOMICS  OF  CONCRETE  MIXING 

Table  39a.     Proportions  of  Materials  in  Concrete 387 

Table  396.     Moduli  of  Rupture  in  Plain  Concrete  Beams 389 

CHAPTER  XLI 

ECONOMICS  OF  MAINTENANCE  AND  REPAIRS 

Table  41a.     Amounts  that  can  Economically  be  Spent  on  Strengthening  Old 

Bridges 418 


ECONOMICS  OF  BRIDGEWORK 


CHAPTER  I 


INTRODUCTION 


Upon  the  scientific  application  of  the  principles  of  true  economy  in  all 
lines  of  activity  will  depend  the  success  of  every  one  of  the  great  nations 
in  the  world-struggle  for  business-supremacy  which  is  about  to  follow  the 
final  close  of  the  Great  War.  This  statement  is  peculiarly  applicable  to 
the  United  States  of  America,  which  is  always  unavoidably  handicapped  by 
the  high  cost  of  labor,  and  at  present  is  unnecessarily  and  stupidly  ham- 
pered by  an  epidemic  of  strikes  and  a  wide-spread  insane  desire  to  shorten 
working  hours  far  below  the  minimum  limit  requisite  for  adequate  produc- 
tion of  the  necessities  of  life  for  our  own  country  alone. 

Until  mankind  recognizes  that  labor  is  a  blessing — not  a  curse — prog- 
ress will  be  slow,  and  the  development  of  the  world  in  all  fines  will  be 
seriously  impeded.  No  healthy  man  or  woman,  or  even  a  child  of  school 
age,  is  injured  by  eight  hours  per  day  of  fairly-strenuous  physical  or 
mental  exercise,  provided  that  its  character  be  suited  to  the  individual's 
age,  capacity,  and  taste.  When  one  is  healthily  tired  upon  the  expiration 
of  his  daily  task,  he  is  in  condition,  after  a  very  short  rest,  to  enjoy  his  food 
and  recreation;  but  any  person  having  no  settled  occupation  nor  any 
regular  duties  to  perform  is  an  unhappy,  discontented  individual  who  not 
only  spoils  his  own  life  but  also  interferes  with  the  enjoyment  and  well- 
being  of  all  persons  with  whom  he  comes  in  contact. 

A  real  love  for  work  per  se  should  be  inculcated  in  every  child  by  its 
parents  and  teachers;  and  extra  work  should  never  be  given  as  a  punish- 
ment, because  so  doing  would  engender  a  distaste  for  labor.  All  work 
should  bo  made  as  pleasant  and  interesting  as  possible,  not  only  for  chil- 
dren but  also  for  adults ;  and  if  anyone  cannot  learn  to  fike  the  occupation 
to  which  he  has  been  assigned,  the  character  of  his  employment  should 
be  changed  from  time  to  time  until  he  finds  a  niche  into  which  he  fits  com- 
fortably. This  development  of  a  love  for  work  in  the  young  is  specially 
important  in  relation  to  study;  because,  when  an  individual  once  becomes 
truly  interested  in  his  occupation,  be  it  either  mental  or  physical,  his  life's 
battle  is  already  more  than  half-won. 


2  ECONOMICS   OF  BRIDGEWOEK  Chapter  I 

For  several  years  the  U,  S.  A.  has  had  a  unique  opportunity  to  become  in 
all  hnes  the  leading  nation  of  the  world;  but  alas!  it  has  not  recognized 
the  existence  of  this  important  privilege  or  taken  the  steps  necessary  for 
its  utHization.  Latin-America  is  knocking  at  our  door  asking  us  to  do 
business;  the  nations  of  Asia,  Africa,  and  Australasia  are  eager  to  enter 
into  commercial  relations  with  us;  and  the  peoples  of  war-afflicted  Europe 
need  both  our  manufactures  and  our  raw  materials.  But  what  foreign 
business  can  we  do  when  Americans  in  general  are  wiUing  to  work  only  six 
hours  per  day  and  five  days  per  week — and  even  then  with  lessened  effi- 
ciency? That  amount  of  effort  is  insufficient  to  provide  for  home  necessi- 
ties; and,  therefore,  it  is  entirely  inadequate  for  the  development  of  foreign 
trade.  The  beaten  Huns  and  their  deluded  aUies  will  have  to  work  long 
hours  for  many  a  year  to  come,  in  order  to  pay  the  principal  and  interest 
of  the  immense  debts  which  are  a  just  punishment  for  their  iniquitous 
endeavor  to  conquer  the  rest  of  the  world  and  impose  upon  it  their  vicious 
system  of  "kultur";  the  innocent  nations  whom  they  have  despoiled  will 
have  to  labor  just  as  strenuously,  in  order  to  repair  their  damages  and 
repay  the  money  they  were  forced  to  borrow  in  their  dire  struggle  to  main- 
tain national  existence;  and  even  the  people  of  Great  Britain  and  her 
colonies  will  be  compelled  to  work  overtime  to  reduce  their  enormous  in- 
debtedness. While  all  these  peoples  are  laboring  year  in  and  year  out 
early  and  late  for  six  and  even  seven  days  per  week,  what  will  eventually 
happen  to  this  country  if  its  inhabitants  cut  down  the  hours  of  labor  and 
insist  notwithstanding  upon  maintaining  an  extravagant  style  of  living? 
There  is  but  one  answer  to  this  question,  and  that  is  Dire  Disaster! 

Even  should  the  American  populace  awaken  to  the  fact  that  it  is  neces- 
sary for  them  to  work  full  time,  the  difficulty  will  still  not  be  overcome; 
because  the  average  personal  efficiency  of  Americans  in  all  hnes  is  decidedly 
lower  than  it  was  in  ante  helium  days.  This  inexcusable  evil  will  certainly 
have  to  be  corrected;  but  even  then  our  country  will  be  handicapped,  for 
it  must  not  be  forgotten  that,  notwithstanding  our  being  the  one  great 
creditor  nation  of  the  world,  the  war  has  run  us  deeply  into  debt,  and  that 
it  will  require  hard  work  and  plenty  of  it  to  pay  the  interest  and  hquidate 
the  principal. 

What  then  can  be  done  to  increase  our  national  efficiency  to  the  extent 
which  is  necessary  for  the  maintenance  of  the  improved  general  style  of 
living  of  the  so-called  working  classes  and  at  the  same  time  outstrip  our 
competitors  for  the  business  supremacy  of  the  world?  The  answer  to  this 
momentous  question  is  not  difficult,  although  the  accomphshment  of  the 
desideratum  may  prove  to  be  far  from  easy.  It  is  to  develop  throughout 
the  entire  country  to  the  utmost  limit  both  the  theory  and  the  practice  of 
true  economy  in  every  line  of  endeavor.  By  the  expression  "true  econ- 
omy" is  not  meant  depriving  people  of  either  the  necessities  or  even  the 
hixuries  of  lift!  (although,  truth  to  tell,  a  curtailment  of  the  latter  would 
gniatly  aid  in  expediting  the  desired  result),  but  a  universal  increase  in 


INTRODUCTION  3 

personal  efficiency — an  elimination  of  useless  effort — a  systematic,  scien- 
tific study  of  how  best  to  accomplish  all  important  desiderata — and  keep- 
ing usefully  and  efficiently  occupied  all  members  of  society. 

As  almost  all  the  material  progress  of  mankind  is  either  directly  or 
indirectly  due  to  the  work  of  the  engineer,  the  importance  of  increasing  his 
efficiency  is  paramount;  and,  hence,  the  study  and  development  of  the 
science  of  engineering  economics  is  of  prime  importance.  Notwithstanding 
this  incontrovertible  truth,  it  is  a  fact  that  in  times  past  our  universities 
and  technical  schools  have  almost  entirely  ignored  this  fundamental  and 
vitally-important  requirement  of  the  engineering  profession.  Only  a  few 
of  them  provided  in  the  curriculum  any  instruction  at  all  in  technical 
economics;  and  even  these  did  not  attach  to  the  course  anything  like  the 
importance  which  is  its  due. 

A  few  years  ago,  the  Society  for  the  Promotion  of  Engineering  Educa- 
tion, awakening  to  a  realization  of  its  shortcoming  in  this  vital  matter, 
appointed  a  committee  of  four,  of  which  the  author  was  chairman,  to  inves- 
tigate and  report  upon  the  subject  of  "The  Study  of  Economics  in  Tech- 
nical Schools."  After  working  upon  the  question  for  two  years,  the  com- 
mittee reported  unanimously  in  favor  of  the  subject  being  taught  in  all 
technical  courses,  and  indicated  the  ground  that  ought  to  be  covered 
and  the  minimum  amount  of  time  that  should  be  allotted  to  it  in  the 
curriculum.  This  was  as  far  as  the  other  three  members  of  the  committee 
at  that  time  were  willing  to  go;  but  the  author  went  farther  by  submitting 
a  supplementary  report  advocating  the  preparation  of  an  elaborate  treatise 
on  "The  Economics  of  Engineering"  by  a  large  number  of  carefully- 
chosen  specialists  under  the  auspices  of  the  Society.  As,  in  the  author's 
opinion,  this  suggestion  of  his  is  of  national  importance,  he  herewith  repro- 
duces verbatim  the  said  supplementary  report. 

"This  is  by  no  means  a  minority  report,  for  the  writer  thereof  agrees  heartily  with 
all  the  conclusions  of  the  committee,  the  members  of  which  are  now  in  entire  accord 
on  all  matters  considered,  after  having  discussed  at  great  length  many  mooted  points; 
but  it  is  a  supplementary  report,  or  something  in  the  nature  of  a  corollary.  It  is  true 
that  the  fundamental  suggestion  it  contains  was  made  to  the  committee,  but  it  was 
not  deemed  advisable  to  include  it  in  the  formal  report;  hence  the  writer  makes  it 
upon  his  own  responsibility. 

"Briefly  stated,  it  is  that  the  Society  undertake  the  .compilation  into  book  form  of  a 
large  number  of  monographs  to  be  prepared  by  the  most  eminent  American  or  Canadian 
specialists,  one  in  each  division  or  subdivision  of  engineering,  all  of  the  said  mono- 
graphs being  edited  and  introduced  by  a  special  committee  of  the  Society,  and  treating, 
in  as  complete  a  manner  as  practicable,  of  the  economics  of  design  and  construction 
in  the  various  Unes.  The  book  (which  might  very  properly  be  called  'The  Economics 
of  Engineering')  should  begin  with  a  full  'Introduction'  explaining  the  raison  d'etre 
of  the  work,  giving  a  history  of  its  compilation,  and  offering  suggestions  as  to  how 
best  it  may  be  utilized,  both  in  its  own  form  and  in  smaller  derived  books. 

"This  chapter  should  be  followed  by  one  which  treats  fully  of  the  fundamental 
economic  problem  underlying  every  important  engineering  enterprise,  viz.,  its  financial 
probabilities  and  possibilities — in  other  words,  whether  the  project  under  consideration 
would  prove  to  be  a  profitable  investment. 


4  ECONOMICS   OF   BRIDGEWORK  Chapter  I 

"Following  this  should  come,  preferably  in  their  alphabetical  order,  the  before- 
mentioned  treatments  of  the  economics  of  design  and  construction  in  the  various  engi- 
neering specialties. 

"Such  a  treixtise  would  constitute  an  encj^clopiedia  of  practical  information  on  one 
of  the  most  important  features  of  modern  teclmics.  It  would  be  invaluable  to  both 
the  practicing  engineers  and  the  teachers  of  engineering;  also  to  the  better  class  of 
engineering  students,  or  those  of  them  who  are  not  afraid  of  hard  work — especially 
]io.st-graduate  students.  But  in  order  to  make  its  contents  of  use  to  the  average  stu- 
dent, it  would  be  necessary  to  jirepare  from  it  text-books  of  a  simple  character.  Should 
the  Society  favor  having  such  a  treatise  issued  imder  its  auspices,  a  publisher  of  estab- 
lished reputation  could  undoubtedly  be  found  to  finance  the  imdertaking  and  issue 
the  work  at  his  own  expense — preferably  A\'ithout  paying  any  royalty,  in  order  to  keep 
the  selUng  price  down  to  a  minimum. 

"A  short  time  ago,  by  the  request  of  the  Dean  of  the  Engineering  Department  of 
the  University  of  Kansas,  the  writer  prepared  and  delivered  a  course  on  'Engineering 
Economics'  in  three  lectures  to  the  engineering  fa  cult  j^  and  students  of  that  institu- 
tion. The  University  has  lately  published  these  lectures  in  pamphlet  form;  and  the 
writer  has  placed  a  few  copies  thereof  at  the  disposal  of  tliis  meeting.  The  first  lecture 
deals  with  the  fundamental  economic  problem  of  finance  before-mentioned;  the  second 
treats  in  general  detail  of  the  economics  of  bridge  design  and  construction;  and  the 
third  is  a  compilation  of  certain  data  furnished  by  the  courtesy  of  a  number  of  prominent 
specialists,  outlining  in  a  general  way  the  economics  of  design  and  construction  in  their 
specialties.  The  writer  would  be  willing  to  rewrite  and  expand  the  first  lectiu-e  so  as 
to  make  it  serve  for  the  second  chapter  of  the  proposed  treatise;  and  the  second  lec- 
ture could  be  sent  to  each  of  the  chosen  specialists  in  order  to  indicate  the  extent  of 
the  desired  thoroughness  of  treatment  of  his  subject,  and  to  serve  otherwise  as  a  guide 
to  him  in  the  ]ire])aration  of  the  manuscript.  If  it  were  expanded  by  the  writer  so  as 
to  include  the  'Economics  of  Steel  Arch  Bridges,'  it  might  serve  for  the  chapter  devoted 
to  the  specialty  of  bridge  engineering. 

"The  third  lecture,  wlaich  nowhere  aims  at  completeness,  would  prove  useful  in 
suggesting  some  of  the  sahent  topics  which  should  be  covered  in  the  \\ritings  of  a  few 
of  the  specialists. 

"The  preceding  proposal  is  made  with  all  due  deference  to  the  distinguished  tech- 
nical educators  and  practicing  engineers  of  which  tliis  Society  is  so  largely  comjiosed, 
in  the  hojie  that  it  will  meet  with  a  favorable  reception  and  will  prove  to  be  the  means 
of  materially  augmenting  the  amount  of  available  teclmical  knowledge  in  a  line  of 
thought  which  has  not  received,  up  to  the  present  time,  the  consideration  which  is  its 
due. 

"Respectfully  submitted, 

"J.  A.  L.  Waddell, 

"Chairman." 

This  report  was  read  by  the  author  at  an  amiual  nipotin«r  of  the  Society; 
and,  in  response  to  his  suggestion,  a  connnittee  of  three  members  was  a{>- 
pointed  to  consider  and  report  upon  the  jiroposal.  At  the  next  annual 
meeting  that  connnittee  reconnnended  against  the  Society's  fathering 
the  suggested  enter]irise. 

FaiUng  in  this  endeavor,  the  author,  over  a  year  ago,  made  to  the 
National  Economic  League,  of  which  he  is  a  member,  the  suggestion  that 
it  undertake  the  work  which  the  S.P.E.E.  had  refused;  but  the  fii-st- 
mentioned  organization  has  not  j'^et  taken  any  action.  Assuming  that  the 
long  delay  indicates  that  this  society  also  intends  to  "pass  the  buck," 


INTRODUCTION  5 

the  author  has  given  up  the  attempt  to  inthicc  his  brother  speciaUsts  to 
collaborate  with  him  in  the  production  of  the  proposed  treatise  on  "The 
Economics  of  Engineering."  Instead  he  presents  to  the  profession  as  a 
possible  starter  for  such  a  joint  work  this  treatise  on  bridge  economics,  in 
the  hope  that  some  day  American  engineers  will  awaken  to  the  importance 
of  having  available  either  a  number  of  small  books  on  the  economics  of  the 
various  specialties  or  else  a  joint  work  similar  to  the  one  which  he  has  advo- 
cated, and  which  appears  at  present  to  be  too  much  in  advance  of  the 
times. 


CHAPTER  II 


GENERAL   ECONOMIC    PRINCIPLES 


The  subject  of  economics  in  engineering  may  properly  be  termed  a  new 
one,  in  spite  of  the  facts  that  for  several  decades  the  leading  specialists,  in 
a  more  or  less  desultory  way,  have  given  the  matter  some  attention  in  their 
designing,  and  that  there  have  been  several  small  treatises  written  upon 
the  mathematical  theory  of  engineering  economics,  notably  Prof.  J.  C.  L. 
Fish's  excellent  little  book  which  bears  that  title,  and  which  eveiy  progress- 
ive engineer  ought  to  read.  Besides  bridgework,  the  only  engineering 
specialty  that  has  received  any  attention  worth  mentioning  in  respect  to 
the  important  question  of  economics  is  railroading — and  that  field  still 
needs  a  vast  amount  of  investigation.  It  is  a  branch  of  engineering  which, 
like  bridgework,  readily  lends  itseK  to  economic  study;  and  it  is  to  be 
hoped  that  ere  many  years  the  economics  of  railroading  in  all  its  branches 
will  be  thoroughly  solved  by  a  number  of  America's  most  able  railroad 
men,  and  that  they  wiU  give  to  the  engineering  profession  the  benefit  of 
their  experience  and  investigations. 

As  far  as  relates  to  engineering,  the  term  "Economics"  has  been  thus 
defined  by  the  author  in  the  ''Glossary  of  Terms"  given  in  "Bridge  Engi- 
neering"— "The  science  of  obtaining  a  desired  result  with  the  ultimate 
minimum  expenditure  of  effort,  money,  or  material."  It  is  upon  the 
basis  of  that  definition  that  this  treatise  is  predicated. 

When  determining,  from  the  standpoint  of  economy,  which  one  is  the 
best  of  a  number  of  proposed  constructions  or  machines,  there  should  be 
computed  for  each  case  the  four  following  quantities,  and  then-  sums : 

A.  The  annual  expense  for  operation. 

B.  The  average  annual  cost  of  repairs. 

C.  The  average  annual  cost  of  renewals. 

D.  The  annual  interest  on  the  money  invested. 

That  one  for  which  the  sum  of  these  items  is  least  is  the  most  economic 
of  all  the  proposed  constructions  or  machines;  but  this  statement  is  ti'uly 
correct  only  when  the  costs  of  operation,  repairs,  and  renewals  are  averaged 
over  a  long  term  of  years;  or  else  for  a  comparatively  short  period  of  time, 
when  the  conditions  in  respect  to  wear  and  deterioration  at  the  end  of  that 
period  are  practically  the  same  for  all  cases. 

The  principal  economic  investigation  which  occurs  in  engineering 
practice  is  that  of  determining  the  financial  excellence  of  a  proposed  enter- 

0 


GENERAL  ECONOMIC   PRINCIPLES  7 

prise.  It  consists  in  showing  by  proper  calculations  its  first  cost,  the 
probable  total  annual  expense  of  maintenance,  repairs,  operation,  and 
interest,  the  advisable  allowance  for  deterioration  or  ultimate  replacement, 
the  probable  gross  income,  and  the  resulting  net  income  that  can  be  used  in 
paying  dividends  on  the  stock  or  other  profits  to  the  promoters.  Whether 
any  proposed  enterprise,  after  being  thus  figured,  will  prove  profitable 
will  depend  greatly  on  the  state  of  the  money  market,  the  size  of  the  proj- 
ect, the  probabilities  of  future  changes  in  governing  conditions,  and  the 
personal  equation  of  the  investor.  Generally  speaking,  if  the  computed 
net  annual  profits  on  the  total  cost  of  the  investment  (over  and  above  all 
expenses  of  every  kind,  including  maintenance,  repairs,  operation,  sinking 
fund,  and  interest  on  all  borrowed  capital)  do  not  exceed  five  (5)  per  cent 
of  the  said  total  cost,  the  project  is  not  attractive;  if  it  be  as  high  as  ten 
(10)  per  cent,  the  enterprise  is  deemed  ordinarily  good;  and  if  it  be  fifteen 
(15)  per  cent  or  more,  the  scheme  is  termed  "gilt-edged."  Small  projects 
necessitate  greater  probable  percentages  of  net  earnings  than  do  large  ones; 
and  any  possibility  of  a  future  reduction  of  income  will  call  for  a  high 
estimate  of  net  earning  capacity.  Finally,  the  measure  of  individual  greed 
on  the  part  of  the  investor  will  be  found  to  be  an  important  factor  in  the 
determination  of  the  attractiveness  of  any  suggested  enterprise. 

Such  investigations  as  the  economics  of  an  important  project  should 
generally  be  entrusted  only  to  engineers  experienced  in  the  line  of  activity 
to  which  the  said  project  properly  belongs;  for  if  they  be  left  to  inexperi- 
enced investigators,  it  is  more  than  likely  that  mistakes  will  be  made  and 
money  lost  in  consequence.  The  professional  men  who  generally  do  such 
work  are  the  independent  consulting  engineers;  certain  speciahsts  retained 
on  salary  solely  for  this  purpose  by  important  organizations,  such  as  rail- 
road companies;  and  engineers  who  are  regularly  in  the  employ  of  large 
banking  houses.  The  work  involved  is  of  such  importance  that  it  usually 
commands  large  compensation — as,  indeed,  it  should;  because  to  do  it 
effectively  demands  not  only  long  experience  but  also  good  judgment  and 
a  vast  amount  of  mental  labor,  both  in  order  to  make  oneself  capable  in 
general  and  so  as  to  consider  thoroughly  all  the  points  embraced  by  the 
special  problem  in  hand. 

How  short  sighted  most  promoters  of  important  projects  can  be! 
They  imagine  they  can  obtain  expert  opinion  of  real  value  without  paying 
for  it;  consequently  they  collect  a  mass  of  scattered  and  divergent  infor- 
mation, which,  in  most  cases,  is  of  no  earthly  use.  Any  project  of  impor-' 
tance  is,  of  necessity,  a  great  economic  problem,  and  ought  to  be  solved 
at  the  very  outset  by  special  engineering  talent  of  the  highest  order. 

A  glaring  example  of  the  utter  folly  of  a  community  in  proceeding  with 
important  engineering  construction  without  first  having  a  thorough  eco- 
nomic study  of  the  problem  made  by  a  competent  specialist  is  given  in 
Engineering  News  of  November  30,  1916.  It  relates  to  the  municipal  water- 
power  enterprise  on  which  the  city  of  Montreal  has  been  busy  for  some 


8  ECONOMICS   OF  BRIDGEWORK  Chapter  II 

years.  Feeling  that  the  work  was  being  sadly  mismanaged,  certain  prom- 
inent Canadian  engineers  ''butted  in,"  investigated,  and  reported  upon 
the  incomplete  project.  They  showed  that  the  $12,000,000  enterprise, 
which  the  city  had  about  half  finished,  will  faU  so  far  short  of  returning  a 
profit  on  its  cost,  and  that  it  has  so  many  serious  defects,  that  it  will  be 
far  better  for  the  community  to  lose  aU  it  has  thus  far  expended  than  to 
incur  the  additional  outlay  necessary  to  complete  the  work.  A  thorough 
investigation  to  determine  beforehand  whether  the  scheme  would  be 
profitable  would  certainly  have  indicated  the  futility  of  constructing  on  the 
lines  adopted. 

This  fundamental  economic  problem  of  whether  the  proposed  construc- 
tion will  prove  to  be  a  paying  enterprise  is  often  one  of  extreme  complica- 
tion, involving,  perhaps,  a  determination  of  the  character  of  the  pro- 
posed improvement,  a  choice  of  sites  or  routes,  a  selection  of  uses,  a 
consideration  of  aesthetics,  an  opinion  on  type  or  style  of  construction,  a 
question  of  ultimate  durability,  a  study  of  greatest  possible  convenience,  a 
prevision  of  serious  opposition,  a  prognostication  of  future  conditions, 
an  anticipation  of  prospective  structural  modifications,  and  a  safe  estimate 
of  cost.  The  best  way  to  illustrate  such  complication  is  by  presenting  a 
few  examples  of  actual  cases,  either  pending  or  already  solved.* 

Case  I 

There  is  in  contemplation  a  project  for  building  a  long,  high,  and 
exceedingly  expensive  bridge  across  San  Francisco  Harbor  so  as  to  connect 
the  city  of  San  Francisco  with  the  cities  of  Oakland,  Berkeley,  and  its  other 
suburbs.  This  project  has  been  a  dream  for  at  least  a  decade;  but  it  is 
not  an  idle  dream,  because  some  day  in  some  manner  or  other  it  is  certain 
to  be  realized.  Some  ten  years  ago  the  author  prepared  a  report  for  a 
banker  on  the  feasibility  of  the  project,  the  necessity  for  the  structure,  the 
possible  revenue  from  its  use,  and  its  approximate  cost;  and  since  then 
several  other  engineers  have  made  independent  studies  of  the  problem. 

*  These  examples  are  copied  verbatim  from  Lecture  No.  1  of  the  author's  series  of 
lectures  on  "Engineering  Economics"  delivered  early  in  1917  to  the  Engineering  Alumni 
Association  of  the  University  of  Kansas.  Three  only  of  the  five  illustrative  cases,  viz., 
those  pertaining  to  bridges,  have  been  reproduced.  In  respect  to  Case  2,  it  is  of  interest 
to  note  that  the  suggested  economic  study  has  since  been  made  by  a  Board  of  Advisory 
Engineers  consisting  of  Col.  Bion  J.  Arnold  as  terminal  expert,  Mr.  J.  Vipond  Davies 
as  tunnel  expert,  and  the  author-as  bridge  expert.  Their  joint  report  was  finished  and 
presented  early  in  1919;  but  its  contents  have  not  yet  been  made  public.  All  of  the 
items  mentioned  were  given  full  consideration;  and  the  difficult  question  of  how  to 
tunnel  through  soft  material  at  an  unprecedented  depth  was  solved  in  a  masterly 
manner  by  Mr.  Davies.  It  is  hoped  by  the  writers  of  the  report,  which  consists  of  some 
600  tyf)e-written  pages  and  a  large  volume  of  folded  blueprints,  that  it  will  be  iniblished 
ere  long  by  the  city  of  New  Orleans;  because  it  would  provide  the  engineering  profession 
with  a  good  example  of  how  to  prepare  a  complicated  economics  study  of  a  (H)miilex  sub- 
ject ui)on  an  unusually  large  scale,  and  how  to  solve  several  new  and  difficult  engineering 
problems. 


GENERAL   ECONOMIC    PRINCIPLES  9 

The  communities  interested,  however,  have  taken  as  yet  no  sensible  step 
towards  making  a  thorough  study  of  the  question. 

Practically  none  of  the  governing  conditions  are  satisfactorily  known; 
and,  judging  by  present  indications,  it  is  likely  to  be  a  long  time  before  they 
will  be,  unless,  perchance,  the  leading  citizens  of  the  various  communities 
concerned  bestir  themselves  and  prevail  on  their  ruling  bodies  to  join  forces, 
raise  the  requisite  funds,  choose  an  engineer  of  national  reputation  (or, 
preferably,  a  board  of  three  such  engineers),  arrange  to  allow  him  or  them 
adequate  compensation  for  expert  services  and  all  the  money  necessary  for 
borings  and  other  investigations,  accord  ample  time  for  the  entire  work, 
and  thus  obtain  a  report  that  will  settle  finally  all  the  important  economic 
and  technical  points  involved  in  the  proposition. 

The  main  features  to  determine  are  as  follows,  the  hsting  being  done 
according  to  relative  importance: 

First.  The  probable  gross  incomes  from  all  practicable  combinations 
of  the  various  sources,  year  by  year  for  a  long  term  of  years,  and  the  pro- 
portion thereof  that  is  likely  to  prove  net  in  each  combination. 

Second.  Based  upon  the  result  of  this  investigation,  the  determination 
of  the  extreme  superior  limit  of  cost  for  the  structure  for  each  combination 
of  the  different  kinds  of  traffic. 

Third.  In  view  of  the  great  depths  of  water  in  the  harbor,  what  one  or 
more  of  the  various  proposed  or  possible  sites  might  be  utilized  for  building 
a  bridge  within  the  several  ascertained  limits  of  cost. 

Fourth.  Of  what  kind  of  traffic  it  is  advisable  that  the  proposed  bridge 
should  take  care. 

Fifth.  The  character  of  the  foundation  soil  as  determined  beyond  all 
doubt  by  making  proper  borings,  and  the  settlement  of  best  depths  for  all 
pier  foundations. 

Sixth.  The  various  requirements  of  the  U.  S.  Government  in  respect 
to  minimum  span-lengths,  vertical  clearances,  and  temporary  obstruction 
of  waterway  for  each  proposed  crossing. 

Seventh.  The  minimum  clear-headway  which,  for  a  combination  of  all 
reasons,  it  is  expedient  to  adopt  for  each  proposed  crossing;  and  the  choice 
between  a  bridge  with  and  a  bridge  without  an  opening  span  or  opening 
spans. 

Eighth.  A  safe  estimate  of  total  cost  of  structure  for  each  layout  that 
proves  to  be  feasible,  and  the  corresponding  estimates  of  cost  of  operation, 
maintenance,  repairs,  etc. 

Ninth.  The  time  required  for  completion  of  construction  of  the 
structure  for  each  feasible  layout. 

After  all  these  points  have  been  settled  and  embodied  in  a  report,  it 
will  be  easy  to  determine  finally  whether,  either  at  the  present  time  or 
within  a  certain  number  of  years,  it  will  be  practicable  or  advisable  to  build 
the  proposed  structure;  where  it  should  be  located;  what  traffic  it  should 
carry;  how  long  it  will  take  to  build  it;  what  it  will  cost  for  construction, 


10  ECONOMICS   OF   BRIDGEWORK  Chapter  II 

maintenance,  and  operation;   and  how  the  necessary  funds  are  to  be  pro- 
vided. 

The  actual  conditions  for  the  proposed  San  Francisco  Harbor  bridge, 
as  well  as  they  can  be  stated  at  present,  are  as  follows : 

A.  There  is  a  large  possible  income  from  passenger  traffic,  mainly  from 
commutors  who  now  use  the  ferry,  most  of  which  traffic  would  soon  be 
diverted  to  the  structure,  provided  that  truly-rapid  transit  thereon  be 
furnished  at  all  times;  and  the  said  income,  under  present  conditions, 
would  be  large  enough  to  warrant  the  building  of  an  open-decked,  double- 
track,  electric-railway  bridge  that  would  carr}^  no  other  kind  of  traffic. 

B.  There  is  a  rapidly  increasing  amount  of  automobile  traffic  now  cared 
for  by  the  ferry;  and  this,  undoubtedly,  would  be  augmented  materially 
by  the  superior  and,  possibly,  cheaper  service  of  the  bridge;  nevertheless 
it  is  doubtful  whether  it  would  be  large  enough  to  warrant  the  building  of 
separate  passageways  with  paved  floor  and  the  necessarily-greater  carry- 
ing capacity  of  the  trusses.*  It  would  be  out  of  the  question  to  let  the 
automobiles  use  the  same  space  as  the  electric  trains;  for  such  an  arrange- 
ment would  prevent  the  rapid  transit  of  the  latter. 

C.  There  is  an  immense  amount  of  freight  crossing  the  water;  but,  for 
two  reasons,  it  does  not  appear  probable  that  it  would  ever  be  economical 
to  transport  it  over  a  bridge.  The  first  reason  is  the  great  height  to  which 
both  it  and  its  containing  vehicles  would  have  to  be  hfted,  and  the  con- 
sequent expense  of  such  hfting.  The  second  is  the  greatly  augmented  cost 
of  structure,  due  to  the  far  larger  five  loads  for  both  the  floor  system  and 
the  truoses,  which  the  carrying  of  such  freight  would  necessitate.  It  would 
probably  be  more  economical  either  to  transfer  the  freight  by  ferry, 
as  is  done  at  present,  or  to  carry  it  by  rail  around  the  south  end  of 
the  Bay. 

D.  There  is  at  certain  seasons  a  large  amount  of  passenger  traffic  to 
and  from  San  Francisco  by  certain  trans-continental  raih'oads;  hence  the 
question  arises  whether  the  passengers  should  be  carried  across  in  the 
steam-railway  cars  on  which  they  travel  or  whether  they  should  go  over  in 
the  electric-railway  cars.  The  objection  to  the  latter  method  is  the  indi- 
vidual trouble,  inconvenience,  and  loss  of  time  for  each  passenger;  while 
the  objection  to  the  former  is  the  increased  cost  of  structure  due  to  the 
difference  in  the  live  loads  between  steam-railway  cars  and  electric-railway 
cars.  Of  course,  the  former  cars  would  have  to  be  hauled  in  short  trains  by 
electric  motors,  so  as  to  avoid  the  excessive  concentrated  loading  from  the 
heavy  steam-locomotives. 

E.  The  most  direct  route  for  the  crossing  is  from  Telegraph  Hill  to  the 
outer  end  of  Goat  Island,  and  thence  to  near  the  Oakland  Pier;  and  this  k 
the  one  to  which,  until  quite  lately,  most  attention  has  been  paid.     Th 
main  objections  to  it  arc  as  follows: 

*  Sinnc  this  was  written,  the  immense  development  of  automobile  travel  and  motor- 
truck trafric  throughout  the  entire  country  might  reverse  (his  economic  conclusion. 


GENERAL  ECONOMIC   PRINCIPLES  11 

First.  The  depth  of  water  between  the  city  and  Goat  Island  is  excess- 
ive, thus  making  the  pier  foundations  very  expensive. 

Second.  A  large  proportion  of  the  steamers  using  the  harbor  would 
have  to  pass  under  the  structure. 

Third.  The  War-Department  requirements  in  respect  to  both  hori- 
zontal and  vertical  clearances  would  be  excessive  for  this  location,  because 
of  the  large  number  of  vessels  passing;  and,  in  consequence,  the  cost  of 
structure  would  be  greatly  augmented. 

F.  By  locating  further  inside  the  Bay,  the  depth  of  water  would  be 
reduced  to  a  reasonable  amount,  and  the  number  of  vessels  passing  the 
structure  would  be  comparatively  small.  In  fact,  the  farther  back  from 
the  harbor-entrance  the  structure  is  located,  the  smaller  will  be  the  depth 
of  water  and  the  fewer  will  be  the  passing  vessels.  On  the  other  hand, 
though,  the  greater  will  be  the  total  length  of  structure,  the  farther  from 
the  center  of  population  will  be  its  city  end,  and  the  greater  will  be  the 
distance  which  the  passengers  will  have  to  travel. 

G.  Practically  nothing  is  known  about  the  characters  of  founda- 
tions that  would  be  encountered  at  the  various  proposed  locations;  and  no 
provision  has  been  made  for  money  to  make  the  necessary  borings. 

H.  It  is  impracticable  to  obtain  a  final  decision  concerning  required 
span-lengths  until  a  bona  fide  design,  properly  backed,  has  been  presented 
to  the  War  Department  for  approval. 

I.  In  regard  to  minimum  clear-headway,  it  is  probable  that  the  farther 
inside  the  harbor  the  location  the  less  the  requirement,  because  the  smaller 
and  less  important  would  be  the  passing  craft,  and  the  fewer  the  number 
thereof.  Some  of  them  might  be  forced  to  lower  topgallant  masts  in  order 
to  pass  beneath  the  structure. 

J.  There  would  be  a  serious  objection  to  any  opening  span,  because  of 
the  delay  which  would  be  involved  by  its  operation.  The  real  raison 
d'etre  of  the  structure  is  rapid  transit,  hence  to  interfere  with  that  in  any 
way  would  be  highly  objectionable. 

K.  The  total  cost  of  structure  would  decrease  to  a  certain  point  as  the 
location  is  moved  up  the  harbor,  because  of  cheaper  foundations  and  the 
consequently  shorter  spans;  but  beyond  the  said  point  it  would  increase 
because  of  the  greater  length  of  bridge. 

L.  The  more  expensive  the  structure  the  longer  will  be  the  time  re- 
quired to  build  it;  hence  it  may  be  concluded  that  one  of  the  inner-harbor 
locations  would  need  much  less  time  for  completion  of  bridge  than  the 
Goat-Island  layout.  This  matter  of  time  for  completion  of  structure 
possesses  a  double  importance,  because  any  delay  increases  the  item  of  cost 
due  to  interest  during  construction;  and  by  postponing  the  inception  of 
operation  it  involves  a  loss  of  income  from  use. 

From  the  preceding  it  is  evident  that  the  solution  of  the  initial  economic 
problem  in  connection  with  the  proposed  San  Francisco  Harbor  bridge  is 
one  of  considerable  complication. 


12  ECONOMICS   OF   BRIDGEWORK  Chapter  II 

Case  II 

The  City  of  New  Orleans  for  many  years  has  had  under  consideration 
the  building  of  a  combined  railway  and  highway  bridge  across  the  Miss- 
issippi River;  and  within  the  last  few  years  the  project  has  been  seriously 
contemplated. 

Some  two  decades  ago  the  late  CoUis  P.  Huntington,  President  of  the 
Southern  Pacific  Railway  Company,  and  his  consulting  engineer,  the  late 
Dr.  Elmer  L.  Corthell,  made  an  investigation  of  the  scheme  of  building  at 
that  place  a  double-track  railway  bridge;  and  they  called  in  as  advisory 
engineers  the  author  and  his  brother,  Montgomery,  to  estimate  upon  the 
cost  of  a  low  bridge.  The  death  of  Mr.  Huntington,  which  occurred  shortly 
afterwards,  caused  the  project  to  be  dropped;  and  it  was  never  revived. 
The  author's  joint  study  was  made  with  considerable  thoroughness.  It 
involved  the  solution  of  two  or  three  problems  of  great  magnitude  that  were 
new  to  the  engineering  profession,  the  principal  economic  one  being  a 
comparison  of  costs  of  a  high  bridge  and  a  low  bridge.  The  result  was 
decidedly  in  favor  of  the  latter. 

The  problem  now  facing  the  city,  however,  is  much  more  complicated, 
involving,  as  it  does,  a  combination  of  steam-railway,  electric-railway, 
vehicular,  and  pedestrian  traffics.  There  is  a  choice  between  two  loca- 
tions, one  near  the  center  of  the  city  and  the  other  several  miles  further  up- 
stream— in  fact,  some  intermediate  locations  might  have  to  be  considered. 
There  is  a  sentiment  among  certain  prominent  citizens  favoring  a  tunnel 
rather  than  a  bridge;  and,  on  that  account,  the  question  of  bridge  versus 
tunnel  will  have  to  be  considered,  notwithstanding  the  fact  that  the 
difficulties  presented  by  the  tunnel  proposition  are  almost  insurmountable 
in  view  of  the  present  status  of  engineering  knowledge  and  experience. 

The  question  of  high-bridge  versus  low-bridge  will  have  to  be  thoroughly 
thrashed  out  in  order  to  please  the  public,  although  any  truly-experienced 
engineer  would  determine  very  quickly  in  favor  of  the  latter,  irrespective 
of  the  possible  opposition  of  the  river  interests  and  even  that  of  the  War 
Department. 

The  economic  method  of  handling  the  combination  of  the  various  kinds 
of  traffic  would  require  some  study  to  determine;  and  the  best  m(>ilu;(l 
might  vary  with  the  location  of  the  structure. 

The  style  and  dimensions  of  the  moving  span— whether  swing,  bascule, 
or  vertical  lift — and  the  sizes  of  the  clear  opening  or  openings  are  mooted 
points  involving  a  consideration  of  economics  and  other  important  matters. 
This  (}uestion  is  complicated  by  the  fact  that  the  requirements  ought  to  be 
dependent  on  the  location;  because  at  the  upper  one  there  would  be  very 
few  vessels  passing,  while  at  the  lower  one  there  would  be  many. 

The  unpre(xxlented  depth  for  the  pier  foundations  involves  an  economic 
study  in  order  to  ascertain  the  best  method  of  sinking  and  founding. 

The  facilities  for  freight,  passenger,  and  vehicular  traffic  afforded  by 


.     GENEEAL   ECONOMIC    PRINCIPLES  13 

the  several  proposed  crossings  would  affect  the  total  earnings  of  the  struc- 
ture; hence  this  feature  should  receive  special  attention. 

The  grade  and  alignment  for  any  proposed  crossing  are  factors  that 
must  be  included  in  the  economic  study,  because  they  affect  the  cost  of 
handling  the  traffic;  and  the  matter  of  right-of-way  may  prove  an  impor- 
tant consideration. 

The  property  damages  involved  by  the  approaches  to  the  structure  and 
by  the  shifting  of  existing  tracks  would  differ  materially  in  cost  at 
the  various  possible  crossings,  hence  this  feature  is  one  involving  eco- 
nomics. 

The  choice  between  single-deck  and  double-deck  entails  a  consideration 
of  economics  that  may  prove  to  be  of  some  importance. 

After  determining  the  various  kinds  of  traffic  to  take  care  of,  there 
remains  the  economic  problem  of  deciding  upon  the  live  loads  for  the 
various  parts  of  the  structure.  If  these  are  made  too  high,  there  is  a  waste 
of  material  involved,  and  the  bridge  enterprise  will  forever  after  be  bur- 
dened with  an  unnecessarily  large  annual  interest  to  be  paid  on  that 
account;  but  if  they  are  made  much  too  low,  the  life  of  the  structure  will 
be  curtailed.  The  saving  clause,  however,  in  respect  to  this  adjustment  is 
that,  ordinarily,  a  steel  bridge  does  not  have  to  be  removed  because  of 
overloading  until  the  metal  thereof  is  actually  stressed  at  least  fifty  (50) 
per  cent  more  than  the  permissible  intensities  of  working  stresses  given 
in  standard  specifications  for  design. 

This  general  problem  of  the  proposed  New  Orleans  bridge,  while  not  so 
complicated  as  that  of  the  proposed  San  Francisco-Harbor  structure,  is  of 
an  intricate  nature,  and  will  demand  for  its  solution  engineering  ability 
and  experience  of  the  highest  order. 

Case  III 

There  is  given  in  "Bridge  Engineering"  in  the  chapter  on  "Reports" 
on  pp.  1575  to  1581,  inclusive,  an  economic  study  for  the  replacement  of  a 
bridge  over  the  Mississippi  River,  which  illustrates  some  of  the  economic 
questions  that  arise  in  a  consulting  bridge  engineer's  practice.  In  that 
case  the  point  at  issue  was  whether  it  would  be  best  to  build  a  single-track 
or  a  double-track  bridge  or  to  arrange  for  the  conversion  at  some  future 
time  of  a  single-track  structure  into  a  double-track  one.  Five  methods  of 
doing  the  latter  were  suggested,  and  the  estimates  of  their  total  first  costs 
were  made ;  then,  at  an  assumed  rate  of  interest,  a  table  was  prepared  show- 
ing the  total  cost  of  each  structure  plus  compound  interest  thereon  for 
periods  of  five  years,  up  to  the  limit  of  forty  years.  That  table  indicates  at 
a  glance  the  comparative  economics  of  all  five  methods  at  any  of  the  five- 
year  periods.  A  diagram  prepared  from  the  said  table,  of  course,  would 
be  preferable,  as  it  would  show  more  readily  the  comparison  at  any  inter- 
mediate period. 


14  ECONOMICS   OF   BRIDGEWORK  Chapter  II 

In  comparing  the  economics  of  several  methods  of  accomplishing  the 
same  result,  the  author  has  advocated  the  method  of  computing  and  con- 
trasting the  total  annual  costs,  including  interest  on  first  cost,  upon  the 
assumption  that  all  the  money  needed  for  the  construction  had  been  bor- 
rowed; and  this  is  the  most  logical  method,  although  in  his  practice  he  has 
sometimes  adopted  other  methods — mainly  to  please  his  chents.  Some 
chents  want  to  see  figures  of  total  cost  instead  of  estimates  of  annual  ex- 
pense; and,  under  such  a  condition,  it  is  necessary  to  sum  up  for  each  case 
all  annual  expenses  except  interest,  ascertain  what  amount  of  money  would 
produce  this  sum  by  simple  interest  at  current  rates;  and  add  that  amount 
to  the  total  first  cost.  The  case  giving  the  least  grand  total  would  be  the 
economic  one. 

An  effective  method  of  contrasting  several  differing  types  of  construc- 
tion for  their  economics  is  that  used  in  Case  III,  viz.,  to  assume  a  number  of 
future  dates,  preferably  those  at  which  certain  large  expenditures  would 
probably  have  to  be  made  for  renewals  or  repairs  of  perishable  portions, 
and  compute  the  grand  total  cost  to  each  date  for  each  proposed  structure 
under  the  assumption  that  it  is  then  put  into  perfect  condition,  and  allow- 
ing standard  compound  interest  not  only  on  the  first  cost  but  also  on  all 
annual  expenditures.  A  comparison  of  these  grand  total  costs  at  the 
several  dates  adopted  will  indicate  clearly  which  is  the  most  economic  of 
all  the  types  of  construction  compared. 

To  those  who  have  a  penchant  for  using  mathematical  formulsB,  the 
following  economic  treatment  will  appeal.  It  was  evolved  some  forty 
years  ago  by  Ashbel  Welsh,  past-president  of  the  American  Society  of 
Civil  Engineers. 

To  Find  the  Comparative  Economy  of  Two  Bridges  of  Different 
Cost  and  Durability,  that  will  Answer  the  Same  Purpose 
Equally  Well  While  They  Last 

"Let  C  be  the  cost  and  assumed  real  value  of  one  of  them,  T  the  time  it  will  last,  a 
the  compound  interest  on  one  dollar  for  that  time,  at  whatever  rate  money  is  worth 
to  the  party  pa3'ing  for  the  bridge,  and  L  the  loss  on  the  bridge  at  the  end  of  the  time  T, 
or  the  amount  which  it  would  take  to  make  it  as  good  as  new.  Let  R  be  the  real  value 
of  the  other  bridge,  C  its  cost,  T'  its  duration,  a'  the  compound  interest  on  one  dollar 
for  that  time,  and  L'  the  loss  on  the  bridge  at  the  end  of  the  time  T' ,  or  the  amount 
required  to  make  it  as  good  as  new.  And  let  V  be  the  real  value  of  the  bridge  that 
would  last  forever,  if  all  circumstances  should  remain  constant. 

"Now,  supposing  that  the  money  required  for  building  had  been  borrowed  for  an 
indefinite  time,  the  actual  expense  at  the  end  of  the  time  T  to  the  party  paying  for  the 
bridge  which  would  last  forever  would  be  aV;  and  the  actual  expense  at  the  end  of 
the  same  time  for  the  first  bridge,  after  making  it  as  good  as  new,  would  be  aC-\-L. 
These  two  quantities  arc  eciual :  therefore  the  hitherto  unknown  value  of  V  is 

.  "Similarly,  at  the  end  of  the  time  T",  the  expense  for  the  bridge  which  would  last 
forever  would  be  a'V;  and  that  for  the  second  bridge,  after  making  it  as  good  as  new, 


GENEKAL   ECONOMIC   PRINCIPLES  15 

if  the  cost  had  been  the  real  value  R,  would  be  a'R+L'.     As  before,  these  two  values  are 
equal;  and,  therefore, 


F  =  /?+^. 


Equating  the  two  values  of  V  gives 


L  U 

a  a 

and 

a     a 

"  Now,  if  the  value  thus  found  for  R  be  greater  than  the  cost  C,  the  second  bridge 
is  more  economical  than  the  first;  while,  if  it  be  less,  the  first  bridge  will  be  the  more 
economical." 

It  will  be  noted  that  the  foregoing  method  does  not  mention  costs  of 
operation  and  maintenance.  They  can  be  taken  into  account  by  adding 
their  capitalized  costs  to  the  costs  C  and  C. 

Conditions  sometimes  arise  which  render  it  inadvisable  to  adopt  the 
most  economic  of  the  several  compared  types  of  construction — for  instance, 
when  the  promoters  cannot  possibly  raise  the  money  required  to  build 
the  kind  of  structure  which  they  desire,  and,  consequently,  must  content 
themselves,  for  a  time  at  least,  with  one  that  is  inferior.  An  example  of 
this  is  a  proposed  railroad  through  virgin  country,  where  the  cheapest  kind 
of  a  line  will  serve  to  develop  business,  and  will  suffice  for  many  years  to 
take  care  of  the  traffic,  although  uneconomically  as  compared  with  first- 
class  railroads.  Under  such  conditions  an  engineer  possessed  of  sound 
financial  judgment  would  advocate  building  the  line  at  first  as  cheaply  as 
practicable;  adopting  comparatively  heavy  grades,  sharp  curves,  cheap 
ties,  light  rails,  temporary  structures,  earth  ballast,  low-power  locomotives, 
etc. ;  but  paying  strict  attention  to  the  vital  matter  of  thorough  drainage, 
and  studying  in  advance  of  construction  the  question  of  how  the  line  can 
be  improved  later  at  least  expense  and  without  materially  interfering  with 
traffic. 

As  another  illustration  of  this  economic  consideration,  there  might  be 
taken  the  case  of  a  bridge  for  a  crossing  where  there  is  danger  from  washout 
of  falsework.  Here  it  would  be  advisable  to  adopt  a  cantilever  structure 
instead  of  a  layout  of  simple-truss  spans,  notwithstanding  the  fact  that  it 
might  require  considerably  more  metal  and  might  involve  a  higher  pound 
price  for  erection. 

Such  problems  as  these  may  be  deemed  by  some  people  to  be  questions 
of  expediency  rather  than  of  economics;  but  the  author  prefers  to  treat 
them  as  pertaining  to  the  latter,  which  means  that,  in  the  case  first  men- 
tioned, he  would  consider  it  truly  economic  to  build  the  cheap  fine  and 
operate  it  for  a  while  uneconomically  rather  than  to  spend  at  the  outset 
large  sums  of  money  in  order,  later  on,  to  handle  economically  traffic  that 
possibly  might  fail  ever  to  materialize;  and  that  in  the  second  case  it  would 


16  ECONOMICS    OF   BRIDGEWORK  Ch.m>ter  II 

be  in  the  line  of  true  economy  to  be  somewhat  extravagant  in  the  cost  of 
superstructure  so  as  to  avoid  all  possibihty  of  disaster  during  erection. 

In  this  connection  it  should  be  noted  that  it  will  sometimes  be  more 
economic  to  build  a  hght  structure  at  the  outset  and  later  remove  it  and 
replace  it  by  a  heavier  one,  rather  than  to  build  the  heavier  one  at  first, 
provided  that  the  hght  structure  will  serve  the  purpose  adequately  for  a 
number  of  years,  and  that  the  replacement  can  be  done  without  too  serious 
an  interruption  of  traffic.  For  instance,  it  might  be  cheaper  to  build  a 
$50,000  bridge  now  and  replace  it  in  fifteen  years  by  a  bridge  costing  $100,- 
000  than  to  build  the  $100,000  structure  at  first;  for  the  compound 
interest  on  the  $50,000  additional  investment  for  fifteen  years  at  six  per- 
cent amounts  to  $70,000.  It  will  rarely  pay  to  anticipate  traffic  require- 
ments by  more  than  twenty  or  thirty  years,  in  case  that  thus  anticipating 
them  involves  a  large  additional  expenditure. 

In  respect  to  the  economics  of  design  and  construction  of  bridges,  the 
following  general  suggestions  are  pertinent: 

Anticipating  the  Future 

In  all  engineering  work  of  both  designing  and  construction,  true  econ- 
omy necessitates  a  thorough  consideration  of  future  requirements  and  pos- 
sible eventualities,  also  a  provision  for  meeting  the  same.  For  instance,  in 
designing  a  structure  one  should  consider  possible  future  additions  of 
loading  and  how  to  accommodate  them;  and  in  construction  one  should 
anticipate  delays,  floods,  storms,  and  other  possible  difficulties,  and  should 
prepare  his  programme  so  as  to  meet  them  effectively  and  without  any  un- 
necessary expenditure  of  time,  labor,  or  money.  Foresight  of  this  kind  is 
an  important  element  of  success  in  the  career  of  every  engineer. 

First  Cost 

It  must  not  be  forgotten  that  under  the  item  "First  Cost"  must  be 
considered  all  items  of  expense,  of  every  kind  whatsoever,  that  may  be 
incurred  before  the  structure  is  ready  for  operation.  It  should  include  not 
merely  the  ordinary  estimated  cost  of  construction,  oi'  the  amount  of 
money  to  be  paid  to  the  contractor,  but  also  promotion  expenses,  discount 
due  to  sale  of  bonds  below  par,  commissions  or  other  considerations  for 
services  rendered,  interest  on  money  during  construction,  right-of-way, 
rents  and  minor  incidental  expenses  during  construction,  administration, 
legal  expenses,  engineering,  and  a  proper  contingency  allowance. 

Compensating   Factors   in   Economic   Comparisons   and   Frequent 
Wide  Range  of  Economic  Limits 

In  (he  making  of  economic  studies,  assumed  variations  in  proportions  or 
types  will  nearly  always  increase  the  cost  of  certain  factors  and  reduce  that 


GENERAL   ECONOMIC    PRINCIPLES  17 

of  others,  while  the  vakies  of  some  factors  may  remain  unchanged.  The 
costs  of  these  various  factors  tend  to  balance,  so  that  considerable  modifi- 
cations rarely  produce  great  changes  in  total  cost.  This  principle  is  true 
for  all  kinds  of  factors.  For  instance,  in  determining  the  economic  span 
lengths  for  a  truss  bridge,  increasing  the  span-length  augments  the  cost  per 
lineal  foot  for  the  superstructure  and  generally,  but  not  always,  reduces 
that  of  the  substructure.  Again,  in  contrasting  carbon  steel  and  alloy 
steel  for  bridgework,  the  latter  gives  smaller  weights  but  greater  costs  per 
pound.  Also,  in  comparing  railway  decks  of  the  ordinary  wooden  type 
with  ballasted  floors,  the  first  cost  of  the  latter  is  greater,  but  the  expense 
for  its  maintenance  is  less ;  and  this  last  condition  is  generally  found  when 
pitting  steel  bridges  against  reinforced  concrete  ones. 

The  effects  of  variations  in  factors  can  be  well  comprehended  by  a 
study  of  the  various  diagrams  for  Chapter  XVIII,  which  treats  of  the 
economic  span-lengths  for  simple-truss  bridges  on  various  types  of  founda- 
tions at  different  depths  below  the  elevation  of  Low  Water.  The  plotted 
curves  show  costs  per  lineal  foot  for  superstructure,  substructure,  and  the 
total.  It  will  be  noted  that  all  substructure  curves  are  concave  upward, 
that  the  superstructure  records  are  either  right  lines  or  easy  curves  also 
concave  upward,  and  that  the  lines  for  totals  are  generally  very  flat  curves, 
concave  upward.  The  economic  span-length  occurs  where  the  steepness  of 
the  substructure  curve  is  just  the  same  as  that  of  the  superstructure  curve, 
but  it  will  be  noted  from  the  upper  of  the  three  curves  (the  one  for  total 
costs  per  lineal  foot)  that  varying  twenty-five  feet  either  way  from  the 
absolute  minimum  augments  very  slightly,  indeed,  the  total  cost  per  foot, 
and  that  a  variation  therefrom  of  fifty  feet  seldom  increases  the  said  cost 
more  than  two  per  cent.  Furthermore,  the  exact  minimum  is  dependent 
somewhat  upon  the  personal  equation  of  the  designer;  for  such  matters  as 
sizes  of  pier  bases  must  be  determined  largely  by  judgment,  and  a  slight 
variation  in  unit  prices  of  materials  in  place  will  move  the  lowest  point  of 
curve  some  distance  horizontally. 

From  the  foregoing  it  is  evidently  a  waste  of  time  to  split  hairs  when  one 
knows  he  is  near  the  economic  point;  but,  on  the  other  hand,  adopting  a 
span-length  of  450  feet  when  300  feet  is  the  economic  limit  may  sometimes 
add  ten  or  fifteen  per  cent  to  the  total  cost  of  structure,  consequent^  one 
must  make  sure  that  his  adopted  span-lengths  do  not  differ  too  seriously 
from  those  for  truly  greatest  economy. 

There  is  another  economic  fact  that  is  well  worth  noting,  viz.,  that 
whenever  in  reducing  the  span-length,  some  important  part  reaches  mini- 
mum size,  so  that  further  diminution  in  length  will  not  reduce  that  part, 
it  is  practically  certain  that  a  shorter  length  will  not  be  economic. 

In  nearly  all  economic  studies  for  bridges,  the  lighter  the  superimposed 
load  the  greater  will  be  the  economic  length,  whether  it  be  span,  panel, 
stringer-spacing,  or  what-not.  This  is  largely  due  to  the  fact  that,  in  case 
of  any  design,  as  the  distance  in  question  is  reduced,  if  the  loading  were 


18  ECONOMICS   OF  BRIDGEWORK  Chapter  II 

light,  certain  parts  would  more  quickly  reach  minimum  size  than  they  would 
if  the  loading  were  heavier;  and  any  further  material  reduction  would 
prove  uneconomic. 

Systemization 

Quoting  from  "Bridge  Engineering/'  "The  systemization  of  all  that 
one  does  in  connection  with  his  professional  work  is  one  of  the  most  impor- 
tant steps  that  can  be  taken  towards  the  attainment  of  success."  More- 
over, it  is  one  of  the  fundamental  elements  of  economics  in  all  lines  of  work. 

Time  Versus  Material 

Some  designers  in  their  endeavor  to  save  a  small  amount  of  material 
expend  a  large  amount  of  time,  not  only  of  their  own  but  also  of  other 
people's,  which  time  when  properly  evaluated  is  often  greatly  in  excess  of 
the  cost  of  the  material  saved.  Such  economy  as  this  is  false;  and  its 
practice  is  unscientific. 

Labor  Versus  Material 

Similarly,  some  designers  in  an  endeavor  to  cut  down  quantities  in  their 
structures  increase  the  labor  thereon  to  such  an  extent  that  the  material 
saved  is  worth  only  a  small  portion  of  the  value  of  the  extra  labor  ex- 
pended. For  instance,  if  one  were  to  make  a  smaU  pier  hollow,  the  con- 
crete thus  saved  would  not  be  worth  anything  like  as  much  as  the  cost  of 
the  forms  needed  to  construct  the  hollow  space  and  that  of  the  reinforce- 
ment which  would  be  required  in  the  thin  pier  walls. 

Recording  Diagrams 

The  study  of  economics  is  greatly  facilitated  by  the  use  of  diagrams  that 
record  quantities  of  materials,  costs  of  construction,  times  of  operation, 
etc.,  for  varying  conditions.  In  general,  it  may  be  stated  that  American 
engineers  do  not  use  graphics  for  studying  economics  to  the  extent  which  is 
advisable;  and  that  in  this  they  might  learn  something  from  their  European 
brethren. 

Economics  of  Mental  Effort 

Almost  nothing  concerning  this  important  subject  is  taught  in  our 
technical  schools;  and  but  little  is  known  about  it  by  practicing  engineers. 
To  be  a  truly-successful  engineer,  one  has  need  to  study  deeply  the  matter  of 
how  best  and  most  economically  to  utilize  his  mental  forces;  how  to  ac- 
complish the  greatest  amount  of  work  with  the  smallest  expenditure  of 
effort;  how  many  hours  of  woi'k  pvv  day  for  k)ng-continued  labor  will 
effect  the  largest  acconipUshiiKUit;   to  what  extent  men  in  various  lines  of 


GENERAL   ECONOMIC   PRINCIPLES  19 

activity  should  take  vacations,  and  how  these  should  be  spent;  what  are 
the  effects  upon  one's  working  capacity  from  the  use  of  liquor  and  tobacco 
in  both  small  and  large  quantities;  etc.  All  these  are  economic  questions 
of  great  importance;  and  they  need  to  be  given  proper  attention  by  every 
engineer  who  aspires  to  efficiency  in  both  himself  and  his  employees. 

Again,  the  development  of  the  faculty  of  concentration  is  an  economic 
consideration  of  the  greatest  value. 

Labor 

The  scientific  handling  of  labor  is  an  economic  problem  of  the  utmost 
importance,  and  a  treatise  could  well  be  written  on  the  subject.  The 
principal  desideratum  is  to  keep  the  workmen  well,  happy,  and  contented; 
and  the  best  ways  to  do  this  are  to  treat  them  kindly,  make  them  com- 
fortable, feed  and  house  them  well,  amuse  them  in  their  spare  time,  avoid 
working  them  too  long  hours,  pay  them  by  piece-work  when  practicable, 
listen  patiently  to  their  complaints,  right  their  wrongs,  see  that  they  are 
well  taken  care  of  when  they  are  ill  or  injured,  and  evolve,  if  possible, 
some  feasible  method  of  sharing  profits  with  them.  On  the  other  hand, 
though,  drive  them  hard  and  continuously  during  working  hours,  insist 
upon  their  putting  in  overtime  when  the  conditions  truly  require  it,  dis- 
charge instantly  all  insubordinate  or  otherwise  troublesome  men,  dispense 
quietly  with  the  services  of  all  shirkers,  and  insist  that  everybody  put  forth 
his  best  and  most  intelligent  effort  to  effect  the  maximum  of  accomplish- 
ment in  the  minimum  of  time. 


CHAPTER  III 

ECONOMICS    OF   THE    PROMOTION    OF   BRIDGE    PROJECTS 

In  most  cases  the  promoter  of  a  bridge  project  at  the  outset  is  possessed 
of  rather  inflated  ideas  as  to  the  possibilities  for  gain  by  the  materiahzation 
of  his  proposed  enterprise,  and,  in  consequence,  is  inclined  to  be  uneconom- 
ical in  his  layout  of  structure  and  of  the  money  expenditure  therefor.  If  he 
is  to  make  a  success  of  his  venture,  he  should  begin  withojit  delay  an 
economic  study  of  his  problem;  and  in  this  he  will  require  the  aid  of  a  bridge 
specialist  of  wide  experience.  It  will  nearly  always  be  found  advisable  to 
keep  the  first  cost  of  structure  down  to  an  absolute  minimum,  but  arrang- 
ing to  increase  its  capacity  from  time  to  time  as  the  augmenting  business 
warrants.  Generally  this  is  a  necessity,  because  bankers  will  not  furnish 
money  for  an  extravagantly  conceived  proposition;  but  even  if  the  money 
be  available,  it  would  be  bad  policy  to  spend  any  of  it  unavoidably  at  the 
outset,  for  the  reason  that  the  interest  on  the  extra  expenditure,  up  to  the 
time  when  the  facihty  in  question  is  really  needed,  might  amount  to  a  large 
sum  of  money. 

The  promoter  should  investigate  thoroughly  the  possibility  for  traffic 
of  all  kinds,  keeping  his  own  counsel  about  what  he  is  doing,  in  order  to 
protect  himself  from  hold-up  by  property  owners  or  the  malevolent  opposi- 
tion of  possible  rival  promoters.  After  finishing  this  investigation  of  con- 
ditions, he  should,  if  possible,  determine  the  kind  or  kinds  of  traffic  for 
which  the  proposed  structure  should  provide  and  the  probable  amounts 
thereof  that  there  will  be,  both  at  the  outset  and  for  a  long  series  of  years, 
also  the  net  income  it  will  produce. 

The  preliminary  investigations  concerning  the  probable  traffic  and  other 
sources  of  revenue  should  be  made  with  great  care  and  conservatism.  One 
who  is  optimistic  by  nature  is  prone  to  overestimate,  and  no  promoter  is 
of  any  account  at  all  unless  he  is  optimivstic;  hence  he  should  consider  very 
carefully  all  unceitain  matters  connec^ted  with  the  revenue  estimates,  and 
should  endeavor  always  to  err  upon  the  side  of  safety.  Similarly,  in  com- 
puting the  annual  cost  for  maintenance,  repairs,  and  otlicr  like  ex]ienses, 
he  should  be  (;areful  to  omit  no  items  and  to  figure;  each  item  high  enough 
to  be  beyond  criticism. 

After  his  l)i-idge  specialist  has  reported  upon  the  best  type  of  structure 
to  build,  the  first  (^ost  for  the  minimum  amount  of  construction  at  the 
outset,  and  ( h(>  subsequent  increased  costs  for  enlargements  or  betterments, 
the  pi-onioioj-  should  complete  the  economic  study  of  the  enterprise  and 

20 


ECONOMICS    OF    THE     PROMOTION    OF    BRIDGE     PROJECTS  21 

decide  whether  it  is  advisable  to  undertake  the  venture.  If  he  experiences 
any  difficulty  in  making  up  his  mind  as  to  the  kinds  of  traffic  for  which  he 
ought  to  provide,  his  engineer  should  be  able  to  tell  him  approximately  the 
cost  of  structure  to  carry  any  kind  or  combination  of  kinds  thereof;  and, 
knowing  the  probable  receipts  therefrom,  he  should  then  be  able  to  come 
to  a  proper  decision. 

The  question  often  arises  as  to  whether  it  will  pay  to  accommodate 
pedestrian  travel;  and,  in  the  case  of  a  long  structure  carrying  street  cars, 
it  will  not.  In  some  cases,  however,  in  order  to  procure  a  franchise  for 
building  the  bridge,  it  may  be  necessary  to  agree  to  provide  footwalks  for 
pedestrians,  even  if  there  be  very  few  of  them.  In  the  old  days  of  horse- 
propelled  vehicles,  it  was  practicable  for  pedestrians  to  cross  on  the  main 
roadway,  but  to-day  the  rapid  passage  of  automobiles  would  render  such  a 
procedure  exceedingly  hazardous. 

In  the  case  of  a  proposed  combined-railway-and-highway  bridge,  it  is 
often  good  policy  to  floor  over  the  railway  deck  so  as  to  carry  temporarily 
both  trains  and  vehicles,  and  to  provide  for  attaching  brackets  in  the  future 
to  support  the  latter.  Such  an  arrangement  gives  very  poor  service;  but 
it  often  will  suffice  for  a  number  of  years. 

In  the  building  of  a  railway  bridge  only,  the  approaches  may  be  timber 
trestles,  which  have  a  life  of  ten  years,  more  or  less;  and  at  the  end  of  that 
time  they  can  be  replaced  either  with  new  timber  or  by  permanent  con- 
struction. If  the  bridge  be  built  to  carry  a  double  track,  and  if  one  track 
will  take  care  of  the  traffic  for  a  few  years,  a  single  track  can  be  laid  on  the 
two  inner  lines  of  stringers,  and  the  approaches  may  be  single-track  wooden- 
trestles;  or,  if  preferred,  one  side  only  of  the  double-track  structure  can  be 
used,  and  the  temporary  approaches  can  be  built  off-center. 

In  case  of  a  great  scarcity  of  funds,  a  double-track  bridge  can  be  designed 
with  trusses  for  half  live  load  and  partial  dead  load,  and  an  arrangement 
made  in  advance  for  the  future  doubhng  of  trusses.  The  author  evolved 
and  patented  this  detail  many  years  ago,  but  has  never  since  had  occasion 
to  utilize  it  in  actual  construction,  although  he  has  estimated  upon  its 
employment. 

Occasionally  it  is  feasible  to  build  a  portion  of  the  main  bridge  of  perma- 
nent construction  and  the  remainder  of  cheap,  perishable  materials;  and 
this  expedient  may  be  in  the  line  of  true  economy.  A  quarter  of  a  century 
ago  the  author  built  a  bridge  across  the  Missouri  River  between  Council 
Bluffs,  Iowa,  and  East  Omaha,  Nebraska,  on  the  basis  of  part  permanent 
and  part  temporary  construction;  and  later  he  replaced  the  temporary 
portion  with  permanent  spans.  In  the  original  structure  the  cheapening 
of  everything  was  carried  to  the  utmost  legitimate  limit,  in  order  to  come 
within  the  bankers'  appropriation.  The  pivot  pier  of  the  swing  span 
(the  largest  in  the  world  at  that  time,  viz.,  520  feet)  was  made  permanent; 
but  the  span  itself  was  stripped  of  its  cantilever  brackets  for  roadways  and 
sidewalks,  a  portion  of  the  deck  was  floored  over  for  teams,  a  single  track 


22  ECONOMICS   OF   BRIDGEWORK  Chapter  III 

was  placed  at  the  middle  of  the  double-track  space,  and  pedestrians  had  to 
use  the  roadway.  Of  course,  there  could  not  be  railway  and  highway 
vehicles  simultaneously  on  the  structure,  but  the  roadway  was  wide  enough 
for  teams  to  pass  and  for  a  line  of  pedestrians  on  each  side  of  a  railroad  train. 
The  end  piers  of  the  swing  span  and  aU  the  other  piers  were  built  of  piles 
and  other  timbers,  the  flanking  spans  were  of  the  combination  t3^pe,  viz., 
tension  members  of  steel  and  compression  members  of  timber,  and  the 
approaches  were  single-track  timber-trestles  for  the  railway  and  wooden 
approaches  with  fairty-steep  grades  for  the  highway.  This  temporary 
work  was  constructed  so  as  to  last  at  least  eight  years,  and  it  was  used  for 
ten,  when  it  was  taken  out  by  the  author  and  replaced  with  permanent 
construction  for  the  lUinois  Central  Railroad  Company,  which  had  bought 
the  structure  for  its  main-line  entrance  into  the  city  of  Omaha.  The 
temporary  work  here  described  was  aU  so  well  and  thoroughly  done  that, 
when  it  was  removed,  there  were  no  evidences  whatsoever  of  decay  or 
failure.  The  author  is  of  the  opinion  that  it  could  have  been  used  for  six 
or  eight  years  longer  without  the  slightest  danger  of  any  kind.  The 
evolution  of  a  design  such  as  above  described  involves  economics  of  the 
highest  type;  and  the  author  considers  it  to  be  by  no  means  one  of  his  minor 
achievements  in  bridge  designing  and  construction. 

There  is  a  matter  of  economic  importance  which  no  promoter  should 
ever  forget;  and  that  is  the  growing  scarcity  of  timber,  and,  consequently, 
its  greater  future  price.  While  it  may  prove,  temporarily  advantageous  to 
use  it  in  his  bridge,  he  should  make  sure  that  the  metalwork  of  his  super- 
structure is  strong  enough  and  that  the  foundations  of  his  substructure  are 
sufficiently  substantial  to  carry  properly  the  increased  dead  load  of  the 
spans  due  to  the  future  substitution  of  heavy  concrete  for  hght  timber. 


CHAPTER  IV 

EFFECT    ON    ECONOMICS    FROM    VARIATIONS    IN    MARKET    PRICES    OF    LABOR 

AND   MATERIALS 

The  economics  of  bridge  design  are  not  so  greatly  affected  by  variations 
in  prices  of  labor  and  materials  as  is  commonly  supposed,  because  there  is 
a  tendency  for  all  prices  to  rise  and  fall  more  or  less  uniformly.  If  they 
were  to  do  so  exactly,  the  effect  on  the  economics  would  be  absolutely  nil. 
It  is  only  when  the  variations  in  unit  prices  for  the  component  materials  are 
irregular  that  the  economics  of  design  are  affected,  and  then  in  most  cases 
but  shghtly.  It  is  true  that  when  there  is  a  sudden  rise  or  drop  in  the  cost 
of  superstructure  metal  erected,  the  proportionate  change  in  substructure 
prices  wiU  lag  behind;  but  it  is  generally  not  long  before  a  state  of  com- 
parative equilibrium  is  reached,  and  the  variations  in  prices  become 
more  nearly  uniform  as  compared  with  those  that  existed  before  the  change 
occurred. 

So  far  as  economic  span-lengths  for  simple-span  bridges  are  concerned, 
the  practical  effect  is  small  indeed ;  for,  even  though  the  theoretic  economic 
length  be  considerably  changed,  there  is  always  a  rather  wide  range  on 
either  side  of  the  minimum  where  the  costs  are  but  little  higher. 

Of  more  importance  than  this  is  the  effect  upon  the  relative  economics  of 
different  types  of  structures,  especially  those  of  different  materials  such  as 
steel  and  reinforced  concrete.  In  normal  times  the  base  price  of  structural 
metal  fluctuates  from  about  1.15  cents  per  pound  to  about  1.75  cents — it 
even  ran  up  to  2.25  cents  in  1899  and  1900.  The  cost  of  fabricated  struc- 
tural metal  is  subject  to  still  greater  changes.  Freight  rates  in  different 
portions  of  the  country  vary  from  about  0.1  cent  a  pound  to  over  one  cent. 
Local  conditions  may  affect  transportation  and  erection  costs  materially. 
For  the  foregoing  reasons  the  price  of  structural  metal  erected  is  subject  to  a 
variation  of  about  two  cents  a  pound,  entirely  apart  from  causes  influencing 
the  prices  of  other  materials.  For  instance,  in  January  of  1920,  the  price 
of  cement  was  $2.80  a  barrel  in  New  York  and  $2.43  a  barrel  in  San  Fran- 
cisco, while  the  freight  rate  on  structural  metal  was  0.27  cent  a  pound  to  the 
former  point  and  1.25  cents  to  the  latter.  At  the  same  time,  heavy  construc- 
tion timber  cost  nearly  twice  as  much  in  New  York  as  in  San  Francisco; 
and  while  structural  iron  workers  received  only  8  per  cent  more  in  the  for- 
mer than  in  the  latter,  common  labor  was  paid  nearly  50  per  cent  more. 
Sand,  stone,  and  gravel  were  considerably  cheaper  in  San  Francisco  than  in 
New  York.     At  that  period,  therefore,  structural  metal  was  about  one  cent 

23 


,24 


ECONOMICS   OF   BRIDGEWORK 


Chapter  IV 


a  pound  cheaper  in  New  York  than  in  San  Francisco,  whereas  concrete 
and  timber  were  about  40  per  cent  more  expensive  in  New  York. 

Again,  early  in  1915  structural  metal  erected  was  let  in  a  few  cases  as 
low  as  three  cents  a  pound,  with  prices  of  other  materials  correspondinglj^ 
small;  while  about  two  years  later  the  said  metal  erected  was  for  a  short 
time  as  expensive  as  ten  cents  a  pound,  the  prices  of  other  materials  show- 
ing an  increase  of  less  than  50  per  cent.  In  January  of  1920,  structural 
metal  erected  was  quoted  as  low  as  7  cents  a  pound,  while  other  prices 
were  much  higher  than  in  1917.  Economic  comparisons  in  1920  are,  there- 
fore, quite  similar  to  those  in  the  pre-war  period,  while  those  of  1917  were 
decidedly  different  from  those  of  either  of  the  other  dates. 

The  foregoing  examples  are  sufficient  to  indicate  the  fact  that,  when 
close  economic  comparisons  are  to  be  made,  carefully  selected  unit  prices 
must  be  used.  The  statement  at  the  beginning  of  this  chapter  to  the  effect 
that  such  variations  will  seldom  radically  affect  economic  comparisons,  is 
nevertheless  correct.  The  result  of  an  economic  study  made  with  nor- 
mally-balanced unit  prices  will  rarely  be  in  error  by  any  serious  amount. 

This  question  will  be  discussed  further  in  the  various  chapters  deahng 
with  comparative  economics. 

In  connection  with  the  elaborate  series  of  computations  made  by  the 
author  in  the  preparation  of  his  monograph  on  "Economic  Span-Lengths 
for  Simple-Truss  Bridges  on  Various  Types  of  Foundations/'  he  took  occa- 
sion to  figure  three  sets  of  economic  curves  for  low-level,  double-track, 
steam-railroad  bridges  on  sand  foundations,  one  with  normal  unit  prices 
for  all  materials  in  place,  another  for  extremely  high  prices,  and  the  third 
for  extremely  low  prices.  The  various  unit  prices  for  each  case  were  ad- 
justed according  to  the  author's  best  judgment,  based  upon  an  experience 
in  bridge  estimating  extending  continuously  over  a  longer  period  of  years 
than  he  likes  to  acknowledge.  The  results  of  this  comparison  are  given  in 
the  following  table: 

TABLE   4a 

Economic  Span-Lengths  for  Double-Track,   Steam-Railway  Bridges  on  Sand 

Foundations  at  Various  Depths  below  Extreaie  Low-Water 


Depth  of 
Foundation 
below  Low- 
Water 

Condition  of  Material  Market 

Low 

Normal 

Hi-h 

100' 
150' 
200' 
250' 

290' 
330' 
375' 
425' 

275' 
310' 
3G0' 
430' 

275' 
325' 
375' 

425' 

The  slightnoss  in  the  variations  of  these  economic  8]iaii-l(Migths  with  the 
different  coiiditions  of  the  material  market  is  suflicienlly  c^vidcMit  to  warrant 


ECONOMICS   FROM   VARIATIONS    IN   MARKET   PRICES  25 

the  conclusion  that  ordinary  differences  of  unit  prices  will  not  affect  the 
economic  layouts  for  simple-truss  spans  having  piers  on  sand  foundations. 
Similarly  it  might  be  shown  that  the  conclusion  holds  good  for  any  other 
type  of  pier  foundation. 

There  is,  however,  a  case  in  the  late  practice  of  the  author  which  indi- 
cates that  abnormally  high  variations  (for  the  different  component  mate- 
rials of  bridges)  in  the  changes  in  unit  prices  do  sometimes  affect  materially 
the  economics.  At  the  present  time  the  following  pound  prices  for  metal 
erected  in  suspension  bridges  prevail: 

Wire  Cables 23^  per  lb. 

Carbon  Steel S^  per  lb. 

Nickel  Steel 10^  per  lb. 

A  fair  average  for  the  ante-bellum  unit  prices  of  these  materials  is  re- 
spectively 13^,  5,  and  7  cents.  Using  the  averages  for  the  two  kinds  of 
structural  steel  as  representative  market  prices,  and  applying  their  ratio  to 
the  pre-war  price  of  wire  cables  indicates  that  a  proper  present  price  for 
the  latter  in  place  would  be  20  cents.  This  shows  that  these  cables  are 
about  15  per  cent  too  expensive.  As  explained  in  Chapter  XIII,  the  use 
of  existing  unit  prices  instead  of  ante  helium  ones  raised  the  span-length  of 
equal  cost  for  highway  cantilever  and  suspension  bridges  from  1,000  ft. 
to  1,200  ft.,  that  length  for  like  structures  which  carry  a  certain  combina- 
tion of  highway  and  railway  loadings  from  2,190  ft.  to  2,360  ft.,  and  that 
length  for  similar  bridges  subjected  to  only  steam-railway  loading  from 
2,570  ft.  to  2,630  ft.  These  changes  are  of  some  importance,  hence  one 
must  conclude  that  the  economics  of  certain  types  of  bridges  are  materially 
affected  by  abnormally  great  variations  in  the  ratios  of  rise  or  faU  in  the 
unit  prices  of  their  component  constituents. 

The  location  of  a  bridge  may  affect  to  a  certain  extent  its  economic  lay- 
out, especially  for  American  constructions  in  foreign  countries.  For  in- 
stance, the  freight  and  customs  duties  on  superstructure  metal  might  be 
very  high  and  the  importation  of  skilled  erection-workmen  might  be  a 
necessity,  while  the  prices  of  substructure  materials  and  of  i^nskilled 
labor  therefor  might  be  exceedingly  low;  and  with  such  a  combination  of 
conditions  the  economic  span-lengths  would  be  considerably  shorter  than 
those  governing  in  the  United  States. 


CHAPTER  V 

ECONOMICS    OF   ALLOY    STEELS* 

Whether  it  be  economical  or  the  reverse  to  use  for  bridge  construction 
any  particular  alloy  of  steel  instead  of  standard  carbon  steel  will  depend 
upon  three  fundamental  conditions,  viz., 

A.  The  ratio  of  costs  per  pound  erected  of  carbon  steel  and  the 
alloy  steel  under  consideration. 

B.  The  ratio  of  the  elastic  Umits  of  these  two  steels. 

C.  The  type  and  the  span  length,  or  span  lengths,  of  the  structure 
contemplated. 

If  r  (greater  than  unity)  is  the  ratio  of  costs  per  pound  erected  of  the 
alloy  steel  and  carbon  steel,  and  r'  (less  than  unity)  is  the  ratio  of  elastic 
limits  of  the  two  metals,  then  for  primary  truss  members  of  rods  or  bars  the 
economy  in  using  the  alloy  will  depend  upon  whether  the  product  of  r  and 
r'  is  less  than  unity,  or  mathematically 

rr'<l.  [Eq.  1] 

This  criterion  will  not  hold  good  for  spans;  because,  while  the  ratio  of 
intensities  of  working  stresses  for  simple  (unstiffened)  tension  members  of 
untreated  steelf  is  exactly  equal  to  that  of  the  elastic  limits,  the  varying 
ratios  of  the  intensities  of  working  stresses  for  compression  members  and 
for  rigid  tension  members  (on  gross  sections)  differ  materially  therefrom. 
Moreover,  a  certain  portion  of  the  weight  of  metal  in  a  structure  is  not 
affected  by  varying  the  intensities  of  working  stresses.  Again,  the  cri- 
terion would  take  no  cognizance  of  the  reduction  of  dead  load  due  to  the 
smaller  weight  of  steel  involved  by  using  the  alloy.  The  first  and  second 
of  the  variations  mentioned  are  of  opposite  sign  from  the  third,  and,  in 
consequence,  the  tendency  of  the  combination  is  to  offset;  but  the  pre- 
ponderance, except  in  the  case  of  unusually  long  spans,  is  in  favor  of  the 

*  After  this  chapter  was  completed,  its  contents  were  used  as  a  basis  for  a  paper 
presented  to  the  Academic  des  Sciences  of  France,  entitled  "L'Emploi  Economique  dcs 
Alliages  d'Acier  pour  la  Construction  des  Fonts,"  all  quantities  in  both  diagrams  and 
text  being  changed  to  French  units.  The  paper  was  published  in  condensed  form  by 
the  Acad(!niy  on  .July  12,  1920,  and  in  full  by  he  G^iic  Civil  on  July  24,  1920. 

fin  the  case  of  eye-bars  of  treated  steel,  the  intensity  of  working  tensile  stress  is 
taken  as  either  one-half  of  the  elastic  limit  or  one-third  of  the  ultimate  strength — 
whichever  of  the  two  is  the  smaller. 

26 


ECONOMICS   OF   ALLOY   STEELS  27 

first  two,  and  hence  the  criterion  for  very  short  spans,  such  as  plate-girder 
bridges,  will  be  for  average  cases 

rr'< 0.8.  [Eq.  2] 

This  value  really  varies  from  0.75  for  rolled  I-beam  spans  to  0.85  for  the 
longest  plate-girder  spans. 

But  in  the  case  of  very  long  spans  it  is  economical  to  use  an  alloy  when 
r  r'  is  equal  to  or  greater  than  unity.  This  is  because  in  such  spans  the 
dead  load  is  large  in  comparison  with  the  live  load,  even  after  the  latter 
has  been  properly  increased  for  the  effect  of  impact;  and  because,  as  before 
indicated,  the  use  of  the  alloy  cuts  down  the  weight  of  metal  in  the  parts 
of  the  structure  where  it  is  employed,  and  thus  reduces  the  total  dead  load 
to  be  carried  by  the  trusses  of  the  span  or  spans.  The  greater  the  span- 
length  the  more  marked  is  the  economy  of  adopting  alloy  steel. 

In  Figs.  5a  and  56  are  given  the  economic  limiting  values  of  r  r'  for 
simple-span  and  cantilever  steam-railway-bridges.  The  method  of  using 
these  diagrams  and  the  formula  in  Eq.  2  is  very  simple.  It  can  best  be 
illustrated  by  a  few  examples. 

Example  No.  1 

With  standard  nickel  steel  erected  at  7^  per  lb.  and  standard  carbon 
steel  erected  at  5^  per  lb.  will  it  pay  to  adopt  the  alloy  for  plate-girder 
spans?    Here  we  have 

r  =   7^5 

r'  =  35-^60 

and  rr'  =  7/5  X  35/60  =  0.82 

This  is  less  than  the  0.85  given  by  Eq.  2  for  long  plate-girder  spans, 
hence  the  answer  to  the  question  is  affirmative. 

Example  No.  2 

Mayari  steel  with  an  elastic  limit  of  50,000  lbs.  per  square  inch  costs 
5.5^  per  lb.  erected,  while  carbon  steel  is  worth  4^.  Will  it  pay  to  adopt 
the  alloy  for  building  a  double-track  span  of  275  feet?    Here  we  have 

r  =5.5-^4 
/=  35-^50 
and  r  /  =  5.5/4  X  35/50  =  0.96 

Fig.  5a  gives  0.93  as  the  limit,  consequently  the  use  of  that  alloy  under 
the  market  conditions  stated  would  not  be  economic. 


28 


ECONOMICS   OF  BEIDGEWORK 


Chapter  V 


Example  No.  3 

Standard  nickel  steel  having  an  elastic  limit  of  60,000  lbs.  per  square 
inch  is  worth  erected  7.3^  per  lb.  while  carbon  steel  costs  5.1^5.  What  are 
the  economics  of  employing  it  for  building  a  double-track,  simple-truss 
span  of  550  feet?    Here  we  have 

r  =7.3-^5.1 

r'=  35-=-60 

and  r  r'  =  7.3/5. 1 X  35/60  =  0.835 

3^ff        400        500        &00        700        300        900      1000      1100 


JOO      ZOO 


f.5d 


Fig.  5a.     Economic  Limiting- Values  of  rr'  for  ISimplc-Span,  Steam-Railway  Bridges. 


Fig.  5a  gives  1.01  as  the  limit;  hence  the  use  of  the  alloy  would  effect 
considerable  saving. 


Example  No.  4 

In  the  investigation  for  a  proposed  three-span,  cantilever,  railway  bridge 
having  a  main  opening  of  1,550  feet,  it  was  found  that  an  alloy  stool  of  75,000 
lbs.  (ilastic  limit  would  cost  13. 8(^  per  lb.  erected,  while  standard  carbon 


ECONOMICS   OF   ALLOY   STEELS 


29 


steel  erected  could  be  obtained  for  6.3^  per  lb.     What  are  the  economics 
of  the  case?     Here  we  have 

r  =13.8-f-6.3 

r'  =  35^75 

and  r/=  13. 8/6. 3X35/75=  1.02 

m     600     m     MO     1200    m     leoo     mo     2000     2200  2m, 


1200     mo     mo 

LetK^fh  of  Mam  3paps  m  Feef 


V      m      m     MO 
Fig.  5b.     Economic  Limiting- Values  of  rr'  for  Cantilever,  Steam-Railway  Bridges. 


Fig.  56  gives  1.02  as  the  limit,  which  shows  that  the  costs  of  structure 
are  alike  for  the  two  steels. 

In  Figs.  5a  and  5&  the  basis  of  comparison  is  standard  carbon  steel,  and 
the  curves  were  plotted  from  weights  figured  for  spans  actually  com- 
puted and  proportioned.  The  estimates  referred  to  were  those  worked  out 
by  the  author  a  number  of  years  ago  for  his  two  papers,  "  Nickel  Steel  for 
Bridges"  and  its  sequel,  "The  Possibilities  in  Bridge  Construction  by  the 
Use  of  High  Alloy  Steels,"  published  by  the  American  Society  of  Civil 
Engineers  in  1909  and  1915. 


30  '  ECONOMICS   OF   BRIDGEWOEK  Chapter  V 

In  the  latter  paper  the  curves  of  weights  of  metal  for  cantilever  bridges 
were  extended  far  beyond  the  hmits  of  accurate  computations  by  a  method 
specially  evolved  for  the  purpose;  and,  while  the  said  method  may  not  be 
deemed  strictly  accurate,  it  is  truly  logical  and,  in  all  probabiht}^,  close 
enough  for  the  economic  investigations  in  the  making  of  which  its  result- 
ing weights  were  employed.  From  the  weights  plotted  in  the  "speculative 
zone  "  of  Fig.  7  in  that  paper,  and  herein  reproduced  as  Fig.  5c,  has  been  pre- 
pared Fig.  5d,  from  which  can  be  found  the  comparative  economics  of  any 
procurable  or  practically-possible  high-alloy  steels  for  cantilever  struc- 
tures having  main  spans  exceeding  the  longest  yet  constructed,  viz.,  the 
1,800  ft.  span  of  the  Quebec  Bridge. 

The  following  example  will  illustrate  its  use: 

'  Example  No.  5 

What  are  the  comparative  economics  of  standard  nickel  steel  costing 
in  place  8.5  cents  per  pound  and  an  alloy  steel  having  an  elastic  limit  of 
80,000  lbs,  per  square  inch  and  costing  in  place  11.2  cents  per  pound,  for  a 
three-span,  cantilever  bridge  which  has  a  main  opening  of  2,450  feet? 

From  Fig.  5d  we  find  the  comparing  ratios  of  weights,  in  relation  to  a 
hypothetical  steel  having  an  elastic  limit  of  100,000  lbs.  per  square  inch, 
to  be  1.23  and  1.66;  hence,  compared  with  each  other,  the  ratio  of  average 
weights  per  foot  for  the  two  materials  will  be  1.23^  1.66  =  0.74.  The  ratio 
of  pound  prices  erected  is  1 1.2 -^  8.5  =  1.318.  The  product  of  these  ratios 
is  1.318X0.74  =  0.98.  As  this  is  less  than  unity,  the  high-aUoy  steel  is 
more  economic  than  the  standard  nickel  steel,  and  the  saving  involved  is 
about  two  per  cent. 

It  may  be  noticed  that  in  this  last  investigation  there  is  an  imphed 
assumption  to  the  effect  that  the  steel  for  the  structures  is  unmixed,  or,  in 
other  words,  that  carbon  steel  is  not  employed  for  Ught  members  or  minor 
parts.     The  explanation  for  this  is  four-fold. 

First.  In  such  long  spans  it  pays  to  cut  out  every  possible  pound  of 
dead  load. 

Second.  Everything  connected  with  the  structure  being  on  a  stupen- 
dous scale,  there  will  be  no  members  so  light  as  to  be  proportioned  for 
rigidity  and  not  for  strength. 

Third.  In  the  detailing  of  heavy  members  of  alloy  steel,  it  will  gener- 
ally be  advisable  to  use  the  alloy  so  as  to  make  the  details  themselves  as 
strong  as  possible. 

Fourth.  Even  if  there  were  a  small  amount  of  carbon  steel  employed 
in  these  phenomenally  long  and  heavy  bridges,  the  percentage  thereof  in 
any  two  compared  cases  of  alloy  steels  of  different  elastic  limits  would  be 
so  nearly  alike  that  the  reliability  of  Fig.  5c/  would  not  be  affected. 

A  question  has  been  raised  as  to  the  accuracy  of  the  curves  in  Figs.  5a 
and  56,  on  the  plea  that  the  relative  amounts  of  nickel  steel  and  carbon 


ECONOMICS   OF   ALLOY   STEELS 


31 


steel  which  should  be  used  in  a  nickel-steel  span  depend  upon  the  ratio  of 
unit  costs  and  that  of  elastic  limits,  and  are  not  constant.  Thus,  if  the 
excess  unit  cost  of  nickel  steel  were  large,  it  might  pay  to  employ  carbon 


i?^         ^         ^^         ^^         -^^  ^ 

Sfii/ffO^  JO  spvDSpqqi.  ai  vocfg  /o  y  v//  Jdd  /ppj/j/ jo  ff/q^/^M 

steel  in  the  floor  system,  and  even  in  the  posts;  while,  if  the  said  excess 
were  small,  it  might  be  economical  to  use  the  alloy  in  those  parts.  The 
author's  reply  to  this  criticism  is  that  his  experience  in  figuring  with  alloy 


32 


ECONOMICS   OF   BRTDGEWORK 


Chapter  V 


steels  leads  him  to  believe  that  when  they  are  really  worth  considering  for 
any  case,  the  stronger  metal  should  be  used  for  the  floor  system  so  as  to 
lighten  the  dead  load,  even  if  per  se  that  portion  of  the  structure  were  made 
slightly  more  costly,  and  that  carbon  steel  should  be  substituted  for  the 
alloy  steel  only  in  such  places  where,  without  increasing  the  sectional 


/m      2000       2200       2400       2600       2000      3000      3200      3400      3600     3300 
lenijfhs   of  Main   Spans  /o  fief 

Fig.  hd.     Diagram  Showing  Comparative  Economics  of  All  Trocurable,  or  Practically- 
Possible,  High-Alloy  Steels  for  Long-Span,  Cantilever  Bridges. 


area,  the  weaker  metal  would  provide  ample  strength— for  instance,  in  the 
lateral  systems  and  Hghter  posts  of  moderately-light,  short-span  bridges. 

It  was  upon  this  assumption  that  the  author  many  years  ago  accumu- 
lated the  data  upon  which,  substantially,  the  diagrams  given  in  this  chap- 
ter were  prepared;  and  under  like  conditions  they  may  be  relied  upon  abso- 


ECONOMICS   OF   ALLOY   STEELS  33 

lutely.  But  if  there  should  arise  a  case  in  which  the  choice  of  carbon  steel 
or  alloy  steel  for  the  floor  system  is  debatable,  the  said  diagrams  might  be 
considered  as  only  approximately  correct;  and  in  such  a  case  some  special 
computations  of  weights  and  costs  of  metal  might  become  necessary. 

Attention  is  called  to  the  phenomenally  short  time  required  for  the 
solution  of  any  economic  problem  in  the  use  of  alloy  steels  for  bridgework 
by  means  of  Figs.  5a,  56,  and  5d  when  the  elastic  limits  and  the  pound 
prices  erected  of  the  steels  to  be  contrasted  are  known.  Hereafter  it  will 
be  unnecessary  for  anyone  desirous  of  employing  an  alloy  of  steel  in  the 
design  of  a  bridge  to  wade  through  the  two  papers  previously  mentioned, 
or  the  author's  other  writings  on  the  subject  of  alloy  steels,  because  the 
economic  results  of  all  his  previous  investigations  are  concentrated  into  the 
three  diagrams  last  indicated. 

The  use  of  alloy  steel  in  bridgework  is  only  in  its  infancy,  for  thus  far 
there  have  been  very  few  bridges  built  of  it.  In  1903  the  author  began  hig 
economic  study  of  the  question  of  "Nickel  Steel  for  Bridges,"  and  the 
investigation  required  more  than  three  years  to  complete.  He  found  that 
good,  reliable  bridge-steel  could  be  manufactured  with  an  elastic  limit  of 
60,000  lbs.  per  square  inch  by  adding  to  the  usual  charge  of  molten  metal 
3|%  of  nickel;  and  as  a  result  of  his  findings  several  large  bridges  were  con- 
structed of  that  alloy.  A  few  years  later  the  great  demand  for  nickel  in 
the  manufacture  of  armor  plate  for  ships-of-war  enhanced  the  price  of 
that  metal  to  such  an  extent  as  to  make  it  too  expensive  to  employ  in  bridge 
construction;  and  the  advent  of  the  Great  War  in  1914  sent  the  price 
soaring.  Although  the  cessation  of  hostilities  has  decreased  the  demand  for 
the  alloying  metal,  its  price  is  still  unsettled  and  probably  has  not  yet  been 
sufficiently  reduced  to  warrant  its  employment  for  bridges — nor  in  fact, 
has  there  been  any  call  of  late  for  metallic  bridges  of  importance.  Just 
as  soon,  though,  as  the  general  business  of  the  country  attains  once  more 
a  sound  condition,  there  will  be  a  request  for  some  large  bridges  of  long  span, 
because  a  number  of  them  are  even  now  being  seriously  considered;  and, 
when  that  time  arrives,  the  question  of  alloy  steels  for  such  structures  will 
become  a  paramount  issue,  and  either  nickel  or  some  other  suitable  alloy- 
ing agent  or  agents  for  strengthening  bridge  metal  will  be  greatly  in  demand. 

Since  the  time  when  nickel  became  too  expensive  to  use  in  bridges, 
several  alloy  steels,  other  than  nickel  steel,  have  been  either  exploited  or 
suggested,  the  principal  ones  being  Mayan  steel,  purified  steel  manu- 
factured by  the  electro-metallurgical  process,  aluminum  steel,  vanadium 
steel,  and  silicon  steel.  On  account  of  the  great  cost  of  nickel  and  the 
other  alloying  metals,  there  is  a  tendency  on  the  part  of  a  few  American 
bridge  specialists  to  employ  high-carbon  steel  in  important  constructions. 
In  the  author's  opinion,  this  is  a  dangerous  pohcy  to  adopt,  because  high- 
carbon  steel  is  brittle  and,  therefore,  unsuitable  for  bridgework.  He  has 
never  been  willing  to  use  it  in  any  of  his  constructions,  notwithstanding 
the  fact  that  the  specifications  of  his  "De  Pontibus,"  written  in  1897,  per- 


34  ECONOMICS   OF   BRIDGEWORK  Chapter  V 

mitted  its  emplojTnent  in  certain  of  the  larger  members  of  long  fixed-spans, 
but  barred  it  entirely  from  movable  spans. 

In  the  specifications  of  "Bridge  Engineering,"  written  in  1915,  no  high 
steel  is  permitted,  excepting- only  a  certain  grade  of  metal  termed  "machin- 
ery steel,"  for  which  the  limit  of  reduction  of  area  is  35%  and  that  of  the 
elongation  in  two  inches  is  18%,  both  of  which  values  are  somewhat  greater 
than  those  specified  for  high  steel  in  "De  Pontibus." 

Mayari  steel  is  a  natural  alloy  of  nickel-chromium  steel,  containing 
from  1%  to  1.5%  of  nickel  and  generally  from  0.2%  to  0.75%  of  chromium 
(although  occasionally  the  proportion  of  this  last  element  runs  consider- 
ably greater),  with  sulphur  below  0.04%,  phosphorus  below  0.03%,  and 
manganese  as  desired.  The  ore  comes  from  a  deposit  of  some  25,000  acres 
at  Mayari  in  the  province  of  Oriente  on  the  Island  of  Cuba.  On  account 
of  the  large  irregularities  in  the  elastic  Hmit  of  Mayari  steel,  it  is  not  deemed 
safe  to  count  upon  more  than  50,000  lbs.,  but  as  the  nickel  and  chromium 
which  exist  in  the  ore  cost  no  more  than  the  iron,  the  actual  cost  of  manu- 
factured bridge  members  really  ought  to  be  about  the  same  as  for  carbon 
steel,  unless  it  be  that  the  content  of  these  foreign  elements  has  to  be  in- 
creased. It  may  be  that  IMayari  steel  will  prove  to  be  the  basis  of  the 
future  ideal  alloy  of  steel  for  long-span  bridges;  but  it  is  more  likely  that 
the  irregularity  of  composition  of  the  smelted  metal  will  render  its  employ- 
ment for  that  purpose  too  objectionable. 

Thus  far  there  has  been  no  systematic  attempt  to  use  for  bridgework  the 
"purified  steel"  manufactured  by  the  electro-metallurgical  process,  the 
main  objection  to  it  being  that  up  to  the  present  time  it  has  never  been 
produced  in  large  melts  or  on  a  grand  scale,  as  would  be  necessary  if  it 
were  employed  in  steel  structures. 

As  for  aluminum  steel,  it  has  never  even  been  in  the  running,  although 
advocated  for  bridgework  by  a  few  engineers  who  apparently  were  not 
properly  posted  concerning  its  properties. 

At  one  time  the  author  had  the  hope  that  vanadium  steel  might  solve 
the  problem  of  alloy  steel  for  bridgework;  but  from  all  he  can  learn  of  late 
about  that  alloy  it  appears  to  fall  short  in  several  essential  requirements. 

Silicon  steel  in  bridgework  has  been  tried,  and  with  satisfactory  results. 
It  is  about  as  difficult  to  manufacture  as  other  alloy  steels,  the  elastic 
limit  being  forty-five  thousand  pounds  per  square  inch.  It  has  not  been 
very  much  used  as  yet,  but  those  who  have  tried  it  seem  satisfied  with  the 
results.  It  ought  not  to  be  very  expensive  per  pound,  as  the  alloying 
material  is  not  costly. 

Of  late  the  element  molybdenum  has  been  looming  up  as  a  possibility 
in  the  solution  of  the  high-alloy,  bridge-steel  problem,  but  thus  far  no  ex- 
periments with  it  have  been  made  looking  towards  its  use  in  bridge  con- 
struction. The  author  nowadays  is  indulging  in  a  "pipe-dream"  about 
what  he  has  dubbed  "Nichromol"  steel,  a  prosi>e('tive  alloy  of  nickel,  chro- 
mium, and  molybdenum,  with  an  excess  of  manganese  above  the  amount 


ECONOMICS    OF   ALLOY    STEELS  35 

ordinarily  used  in  steel-making,  as  being  the  ultimate  solution  of  the  said 
problem.  He  is  endeavoring  to  make  the  dream  come  true  by  trying  to 
induce  a  combination  of  miners,  metallurgists,  and  steel  manufacturers  to 
furnish  the  requisite  money  for  an  elaborate  series  of  experiments'  to  find 
an  ideal  high-alloy  of  steel  for  long-span  bridges;  and,  perhaps,  if  he  lives 
long  enough,  he  will  be  successful.  He  feels  confident  that  within  three 
years  after  actually  starting  the  investigation,  with  ordinarily  good  luck 
in  respect  to  governing  conditions,  and  with  a  reasonable  expenditure  of 
money,  he  could  find  how  to  manufacture  the  material  desired  at  a  fairly- 
moderate  pound-price.  A  successful  solution  of  this  problem  would  be 
epoch-making  in  respect  to  the  economics  of  bridgework. 

There  appeared  in  the  New  York  Times  of  February  18th,  1920,  a  notice 
concerning  some  experiments  that  are  being  made  in  France  upon  the 
production  of  high-grade  steels  by  a  modification  of  the  Bessemer  process. 
If  these  experiments  prove  to  be  successful,  the  manufacture  of  the  author's 
proposed  ''Nichromol  Steel"  may  be  readily  materialized.  The  following 
is  the  notice  referred  to : 

Paris,  Feb.  16. — A  revolution  in  the  steel  industry  is  promised  by  four  inventors 
who  are  working  here.  Final  tests  of  their  process  are  now  being  made.  Their  claim 
is  that  hard  steel — nickel,  chromium,  manganese  and  the  other  kinds — can  be  manu- 
factured at  roughly  the  same  cost  as  ordinary  Bessemer  steel,  with  the  sole  added 
expense  of  the  alloys  involved. 

In  a  mill  on  the  northern  outskirts  of  Paris  to-day  five  experiments  were  made 
each  involving  the  production  of  a  ton  and  a  half  of  high-class  steel.  There  was  little 
in  appearance  to  distinguish  the  new  from  the  ordinary  Bessemer  process.  There 
was  an  ordinary  furnace,  packed  with  coal  and  iron.  The  metal  was  fused  at  a  rela- 
tively low  temperature  and  then  passed  to  a  furnace,  where  the  temperature  was  raised 
to  1500^  C.  and  the  impurities  burned  out.  By  the  Bessemer  process  a  relatively 
small  percentage  of  impurities,  chiefly  phosphorus  and  sulphur,  is  eliminated.  The 
result  is  that  Bessemer  steel  is  suitable  for  only  ordinary  work  and  cannot  be  employed 
as  raw  material  for  the  high  grade  steel  necessary  for  many  phases  of  industry. 

The  essential  feature  of  these  experiments  is  that  by  the  addition  of  certain  secret 
substances  and  by  means  of  a  certain  undivulged  process  the  ordinary  Bessemer  steel 
process  can  be  applied  to  produce  steel  as  pure  as  that  derived  electrically. 

These  results  are  predicted  by  the  inventors: 

First,  France  will  be  in  a  position  to  produce  high-grade  steel  at  the  same  cost,  or 
approximately  the  same  cost,  as  ordinary  steel  plus  the  expense  of  the  alloys,  while 
special  steel  containing  no  alloys  can  be  produced  at  the  same  price  as  ordinary  steel. 

Second,  high-grade  steel,  which  hitherto  could  not  be  employed  for  such  ordinary 
purposes  as  railway  rails,  etc.,  now  becomes  available  for  the  everyday  purposes  of 
commerce. 

The  four  inventors  have  been  working  for  more  than  six  months  and  have  satisfied 
themselves  that  the  high-grade  steel  they  produce  answers  to  every  test,  whether  of 
chemical  analysis  or  of  physical  properties,  such  as  hardness,  tensile  stress,  malleabil 
ity,  etc. 

One  of  the  inventors  is  Jules  Lambrecht  of  Herstal,  Belgium,  who  worked  as  a  steel 
expert  for  France  during  the  war.  Another  is  Marc  Antoine,  also  a  Belgian,  known 
as  an  authority  on  railroad  steel.  The  other  two,  whose  names  may  not  now  be  men- 
tioned, are  Frenchmen. 

To-day's  tests  were  attended  by  a  number  of  steel  experts  and  scientists  who  took 


36  ECONOMICS   OF   BKIDGEWORK  Chapter  V 

away  samples  of  the  inventors'  product.  The  presence  of  these  men  attested  the  seri- 
ousness of  the  experiments,  and  it  is  reported  that  the  inventors  may  have  discovered 
a  process  as  valuable  as  that  of  Sir  Robert  Hadfield,  which  is  reserved  for  Government 
use  in  England,  despite  the  demand  on  the  part  of  private  enterprise.  The  French 
inventors  have  no  connection  with  the  Government. 

They  caU  attention  to  the  fact  that  ordinary  Bessemer  steel,  because  of  the  impurities 
of  the  metal,  wears  badly  and  irregularly.  Hard  steel  having  a  much  longer  life  can  be 
made  to  bear  the  same  strains  with  very  much  less  content  of  material,  and  thus  the 
country  that  is  able  to  produce  high-grade  steel  at  the  cost  of  ordinary  steel  will  benefit 
by  the  immensely  increased  output  and  will  be  able,  because  of  superior  methods,  to 
compete  on  very  favorable  terms  with  Great  Britain,  the  United  States  and  other  steel- 
manufacturmg  countries. 

At  a  time  when  the  whole  world  is  in  need  of  steel  of  every  sort,  the  cheapening  of 
the  highest  grades  and  the  reduction  in  the  amount  of  labor  required  to  produce  it  are 
factors  of  capital  importance  in  the  general  work  of  reconstruction. 

It  is  pointed  out  that,  while  the  electrical  process  for  producing  pure  steel  is  excellent, 
it  requires  an  enormous  expenditure  of  energy  and  labor,  and  is  consequent  Ij'  extremely 
costly.  The  Bessemer  process,  on  the  other  hand,  \vhile  relatively  cheap,  has  hitherto 
failed  to  remove  impurities.  What  the  inventors  say  they  can  do  is  to  obtain  pure  steel 
by  the  use  of  the  Bessemer  process  with  slight  alterations. 

Since  the  preceding  was  written  the  author  has  secured  some  informa- 
tion concerning  molybdenum  steel  for  which  he  has  been  searching  during 
the  last  year  or  two,  and  which  had  been  refused  him  by  a  high  authority 
in  the  employ  of  an  automobile  manufacturing  compam' — possibly  with 
the  thought  that,  if  molybdenum  were  adopted  for  bridgework,  there 
would  not  be  a  large  enough  supply  left  for  the  use  of  the  automobile 
industry.  Some  six  months  ago,  however,  the  author  was  so  fortunate  as 
to  secure  from  the  president  of  the  Climax  Molybdenum  Company  of 
New  York  and  Colorado  certain  interesting  general  information  concern- 
ing the  alloying  properties  of  molybdenum,  with  the  promise  of  detailed 
data  as  soon  as  they  could  be  collected  and  formulated  for  publication  in 
pamphlet  form.  In  accordance  with  that  promise,  there  came  to  hand  a 
short  time  ago  an  advance  copy  of  a  booklet  entitled,  "Molybdenum  Com- 
mercial Steels,"  issued  as  a  trade  catalogue  by  the  before-mentioned  com- 
pany. The  work  contains  a  mass  of  detailed  information  about  the  alloy; 
and,  although  the  data  apply  directly  to  steel  for  automobiles,  it  has  proved 
practicable  to  make  from  the  tabular  matter  deductions  indicating  how  the 
said  alloy  might  be  applied  to  bridge  construction.  It  certainly  contains 
sufficient  statistics  to  enable  an  investigator  to  draft  a  programme  of  studies 
and  tests  for  determining  the  best  practicable  combination  or  combinations 
of  molybdenum  and  other  alloying  elements  with  iron  in  order  to  produce 
the  high  alloy  of  steel  for  bridgework  for  which  the  author  has  been  search- 
ing these  many  years. 

While  it  is  true  that  the  publication  is  unijuestionably  a  trade  cata- 
logue for  the  promotion  of  the  sale  of  molybdeiuim,  it  is  i)ointed  out  therein 
that,  in  order  to  avoid  any  undue  rose-coloiing  caused  by  the  natural 
tendency  in  writing  such  a  work  to  "])ui  one's  best  foot  foremost,"  the 
MS.  was  submitted  for  connnent  to  the  officials  and  metallurgists  of  some 


ECONOMICS    OF   ALLOY   STEELS  "37 

of  the  largest  alloy-steel  manufacturers  and  consumers  in  the  United 
States,  with  the  result  that  it  met  with  their  approval — their  experience 
with  the  various  molybdenum-steel  types  described  conforming  to  the 
statements,  facts,  and  figures  set  forth.  Moreover,  the  general  treatment 
of  the  subject  gives  'prima  facie  evidence  of  a  spirit  of  fairness;  and  the 
style  of  work  is  that  of  a  technical  scientist  and  not  that  of  a  promoter. 

Unfortunately,  the  records  all  deal  with  heat-treated  steel,  which,  while 
applicable  for  eye-bars,  is  not  suitable  for  built  members  of  bridges;  but  by 
inquiry  from  the  writer  of  the  pamphlet  the  author  obtained  a  small  amount 
of  data  concerning  tests  of  one  of  the  steels  untreated,  as  well  as  some  results 
of  tests  of  carbon-molybdenum  steel  that  were  made  on  an  accidental  melt 
from  which  chromium  had  unintentionally  been  omitted.  From  the 
same  source  it  was  learned  that  the  proportionate  increase  in  ultimate 
strength  and  elastic  limit  due  to  the  addition  of  molybdenum  is  practically 
the  same  for  untreated  as  for  treated  steels. 

From  the  contents  of  the  pamphlet,  the  additional  information  just 
mentioned,  and  the  author's  previous  experience  with  nickel  steel,  the 
deductions  which  follow  have  been  drawn. 

For  simplification  of  the  discussion,  and  in  order  to  distinguish  readily 
between  the  various  combinations  of  alloying  materials,  the  author  has 
taken  the  liberty  of  evolving  and  using  the  following  nomenclature: 

Carmol  =  Carbon-Molybdenum. 

Chromol  =  Chromium-Molybdenum. 

Nichromol  =  Nickel-Chromium-Molybdenum. 

Nicmol  =  Nickel-Molybdenum. 

Chrovanmol  =  Chromium- Vanadium-Molybdenum. 

Nichro  =  Chrome-Nickel. 

Chrovan  =  Chrome- Vanadium. 

In  order  to  utilize  the  diagrams  of  this  chapter  for  finding  the  economics 
of  molybdenum  as  an  alloying  material  for  bridge  steel,  an  understanding 
will  have  to  be  arrived  at,  in  order  to  determine  properly  the  values  of  r' ; 
because,  while  a  high  intensity  of  working  stress  may  be  employed  for  heat- 
treated  eye-bars,  a[much  lower  one  will  have  to  be  adopted  for  the  untreated 
built-members;  and,  again,  it  would  never  be  legitimate  to  use  a  working 
stress  greater  than  one  third  of  the  ultimate  strength.  In  heat-treated 
steels  the  elastic  limit  generally  falls  but  little  below  the  ultimate  strength, 
hence  it  would  not  do  to  use  one  half  of  its  amount  for  the  working  tensile 
stress  as  is  done  in  the  case  of  untreated  steel. 

As  the  data  concerning  the  untreated  molybdenum  steel  are  rather 
meagre,  it  will  be  necessary  to  make  a  few  approximate  assumptions  in 
determining  the  elastic  limits  and  intensities  of  working  stresses.  For 
instance,  one  is  that  the  proportion  of  untreated  and  treated  steel  in  a 
pin-connected  bridge  will  be  about  as  two  is  to  one.  This  is  fairly  accurate, 
,  and  will  suffice  for  a  preliminary  study  of  which  the  sole  purpose  is  to  indi- 


38 


ECONOMICS    OF    BRIDGEWORK 


Chapter  V 


cate  in  outline  the  final  investigation  it  will  be  necessary  to  make,  in  order 
to  establish  the  suitability  of  molybdenum  steel  for  bridgework,  determine 
the  best  proportions  for  the  alloying  elements,  and  demonstrate  the 
economics  of  the  alloy  in  comparison  with  other  bridge  steels,  both  plain 
and  alloyed. 

From  "Molybdenum  Commercial  Steels"  and  the  before-mentioned 
supplementary  data  furnished  to  the  author  the  following  tables  have 
been  copied  or  prepared: 

Heat-Treated  Chrome  Steel  with  and  without  Molybdenum 


TABLE  5o 

Tensile   Test   on   Chrome    Steel 

Analysis 


Carbon 

Manganese 

Chromium 

Molybdenum 

0,27 

0.63 

0.99 

None 

Physical  Properties.     (1  inch  round) 

Elastic 
Limit 

Tensile 
Strength 

Elongation 
Per  Cent 

Red.  of  Area 
Per  Cent 

130,000 

139,000 

16.5 

58 

TABLE   56 
Tensile  Test  on  Chromol  Steel 
Analysis 


Carbon 


0.26 


Manganese 


0.64 


Chromium 


0.76 


Molybdenum 


0.31 


Physical  Properties.        (1  inch  round) 


Elastic 
Limit 

142,000 


Tensile 
Strength 

151,000 


Elongation 
Per  Cent 

18.5 


Red.  of  Area 
Per  Cent 

62 


ECONOMICS   OF   ALLOY   STEELS 


39 


Heat-Treated   Chrome   Nickel  Steel  with   and  without  Molyb- 
denum 


TABLE  5c 

Tensile  and  Dynamic  Tests  on  Nichro  Steel 

Analysis 


Carbon 

Manganese 

Silicon 

Chromium 

Nickel 

Molybdenum 

0 .  33  av. 

0.5  av. 

0.18  av. 

1.0  av. 

3.27  av. 

None 

Physical  Properties.     (Rolled  Bars  1"  to  2") 


Elastic 
Limit 


116,700 


Tensile 
Strength 


135,200 


Elongation 
Per  Cent. 


19.6 


Red.  of  Area 
Per  Cent 


57.1 


Izod 
Ft.-Lbs. 


61 


Brinell 
Hardness 


270 


TABLE   5d 

Tensile  and  Dynamic  Tests  on  Nichromol  Steel 

Analysis 


Carbon 

Manganese 

Silicon 

Chromium 

Nickel 

Molybdenum 

0.27  av. 

0.6  av. 

0.3  av. 

0 .  86  av. 

2.95  av. 

0.43  av. 

Physical  Properties.     (On  finished  shaft) 

Elastic 
Limit 

Tensile 
Strength 

Elongation 
Per  Cent 

Red.  of  Area 
Per  Cent 

Izod 
Ft.-Lbs. 

Brinell 
Hardness 

130,000 

142,000 

20.5 

65 

67 

303 

40 


ECONOMICS   OF   BRIDGEWORK 


Chapter  V 


Heat-Treated  Chrome- Vanadium  Steel  with  and  without  Molyb- 
denum 

TABLE   5e 

Tensile  Tests  on  Chrovan  Steel 
Analysis 


Carbon 

Manganese 

Chromium 

Vanadium 

Molybdenum 

0.36  av. 

0.5  av. 

0.9  av. 

over  0 .  16 

None 

Physical  Properties.     (1" 

round) 

Elastic 
Limit 

Tensile 
Strength 

Elongation 
Per  Cent 

Red.  of  Area 
Per  Cent 

Brinell 
Hardness 

146,500 

167,500 

16 

54.5 

340 

TABLE   5/ 

Tensile  Tests  on  Chrovanmol  Steel 
Analysis 


Carbon 

Manganese 

Chromium 

Vanadium 

Molybdenum 

0.39 

•    0.4S 

1.06 

0.17 

0.85 

Physi( 

•al  Prop(n'ties.      (1 

i"  round) 

Elastic    ; 
Limit     ! 

Tensile 

Strength 

Elongation 
Per  Cent 

Kod.  of  Area 
Per  Cent 

Brinell 
Hardness 

170,000 

KIO.OOO 

19 

(10 

392 

ECONOMICS    OF   ALLOY   STEELS 


41 


Heat-Tkeated  Nickel  Steel  with  and  without  Molybdenum 


TABLE   5^ 

Tensile  Tests  on  Nickel  Steel 
Analysis 

Carbon 

Manganese 

Nickel 

Molybdenum 

0.30 

0.25 

4.00 

None 

Physical  Properties 

Elastic 
Limit 

Tensile 
Strength 

Elongation 
Per  Cent 

Red.  of  Area 
Per  Cent 

108,000 

120,000 

16 

55 

TABLE   5h 

Tensile  Tests  on  Nicmol  Steel 
Analysis 


Carbon 

Manganese 

Silicon 

Nickel 

Molybdenum 

0.33 

0.25 

0.18 

4.50 

0.58 

Physical  Properties.     (1|" 

round) 

Oil 
Quench 

Elastic 
Limit 

Tensile 
Strength 

Elongation 
Per  Cent 

Red.  of  Area 
Per  Cent 

1450°  F. 
1500°  F. 
1550°  F. 
1600°  F. 
1650°  F. 

164,600 
166,500 
165,100 
164,900 
166,000 

173,800 
176,000 
175,000 
173,300 
174,400 

16.0 

15.5 
15.5 
15.5 
15.0 

53.4 
55.3 
54.0 
55.6 
55.0 

165,000  av. 

175,000  av. 

15.5  av. 

54.7  av. 

42 


ECONOMICS   OF   BKIDGEWORK 


Chapter  V 


Heat-Treated  Carbon  Steel  with  Molybdenum 


TABLE   5i 

Tensile  Tests  on  Carmol  Steel 

Test  No.  1 

Analysis 


Carbon 

Manganese 

Molybdenum 

0.24 

0.69 

0.32 

Physical  Properties 

Elastic 
Limit 

TensUe 
Strength 

Elongation 
Per  Cent 

Red.  of  Area 
Per  Cent 

92,000 

114,000 

20 

66.5 

TABLE   5j 

Test  No.  2 
Analysis 

Carbon 

Manganese 

Molybdenum 

0.17 

0.49 

0.96 

Physical  Properties 

Elastic 
Limit 

Tensile 
Strength 

Elongation 
Per  Cent 

Red.  of  Area 
Per  Cent 

102,000 

135,300 

19.5 

01 

ECONOMICS   OF   ALLOY   STEELS 


43 


Untreated  and  Treated  Chrome  Steel  with  Molybdenum 

TABLE   5k 
Tensile  Tests  on  Chromol  Steel  (Untreated) 
Analysis 


Carbon 

Manganese 

Chromium 

Molybdenum 

0.26 

0.65 

0.95 

0.32 

Physical  Properties 

Diam.  of 
Test  Piece 

Elastic 
Limit 

Tensile 
Strength 

Elongation 
Per  Cent 

Red.  of  Area 
Per  Cent 

1" 

89J00 

116,900 

18.5 

55 

U" 

104,000 

115,000 

17.5 

54 

2" 

75,000 

100,000 

20.5 

60 

TABLE   51 

Tensile  Tests  on  Chromol  Steel  (Treated) 

Analysis 


Diam.  of 
Test  Piece 

Carbon 

Manganese 

Chromium 

Molybdenum 

8 

0.26 

0.65 

0.95 

0.32 

Physical  Properties 


Drawing 
Temperature 

Elastic 
Limit 

Tensile 
Strength 

Elongation 
Per  Cent 

Red.  of  Area 
Per  Cent 

500°  F. 

220,000 

232,000 

12 

48 

1100°  F. 

130,000 

142,000 

20 

63 

44  ECONOMICS   OF   BRTDGEWORK  Chapter  V 

In  making  cost  estimates  for  alloy-steel  bridges,  the  following  unit  prices 
have  been  assumed.  They  are  based  upon  the  market  conditions  govern- 
ing in  March,  1920. 

Ordinary  carbon-steel  work,  erected 8^  per  lb. 

Nickel 40^  per  lb. 

Chromium 22^  per  lb. 

Vanadium    residue    in    steel     (to    include 

wastage) $10 .  00  per  lb. 

.  Molybdenum $  2 .  50  per  lb. 

Heat-treatment  of  eye-bars 1^  per  lb. 

There  will  first  be  determined  from  the  various  diagrams  in  "Molyb- 
denum Commercial  Steels"  the  best  drawing  temperature  for  the  heat  treat- 
ment of  alloy  steels  to  be  used  in  bridgework.  In  modern  alloy-steel  prac- 
tice there  has  come  into  vogue  the  term  "Quality  Number,"  meaning  the 
product  of  the  elastic  limit  in  pounds  per  square  inch  by  the  reduction  of 
area  expressed  in  ratio  to  unity.  This  is  considered  the  criterion  of  excel- 
lence, because  the  maximum  values  of  these  two  quantities  are  desirable. 
As  the  drawing  temperature  is  increased,  the  elastic  limit  drops  and  the 
reduction  of  area  augments,  consequently  that  temperature  which  makes 
the  product  of  the  two  values  a  maximum  probably  gives  the  best  result 
for  combined  strength  and  toughness. 

An  analysis  of  fifteen  diagrams  in  "Molybdenum  Commercial  Steels" 
shows  that  the  average  best  drawing  temperature  is  800°  F.,  it  being  a 
trifle  greater  for  oil  quenching  than  for  water  quenching.  A  higher  draw- 
ing temperature  than  this  seems  to  be  preferable  for  automobile  steel,  in 
order  to  secure  great  toughness  for  resisting  shock;  but  it  gives  very  good 
results  with  steel  having  main  characteristics  suita])le  for  bridge  building, 
the  average  percentage  of  elongation  for  small  test  pieces  being  15.5.  As 
the  principal  standard  bridge  specifications  call  for  an  elongation  of  15 
per  cent  in  specimen  tests  of  nickel  steel,  it  may  be  concluded  that  the 
molybdenum-steel  alloys  above  considered  are  satisfactory  in  respect  to 
this  criterion. 

There  will  next  be  determined,  as  accurately  as  the  rather  meagre  data 
available  will  permit,  for  all  of  the  usual  kinds  of  alloy  steels,  the  economic 
benefit  to  l)e  derived  by  adding  molybdenum  to  the  other  ingredients  of 
the  steel. 

Cakmol  Steel  versus  Carbon  Steel 

From  a  reliable  source  the  author  has  learned  that  the  heat-treatment 
of  carbon-steel  eye-bars  raises  the  elastic  limit  from  30,000  lbs.  per  square 
inch  to  at  least  50, 000  lbs.  per  square  inch,  and  that  the  present-day  cost 
of  the  lieat -treatment  tis  aboiit  one  cent  per  pound. 

Let  us  assume  that  in  a  pin-connected  bridge  the  average  value  in  place 


ECONOMICS   OF   ALLOY   STEELS  45 

for  carbon  steel,  both  treated  and  untreated,  is  8.5^  per  pound,  then  refer- 
ring to  Table  5i,  w(!  shall  have  the  following: 

CArtMOL   STEEL 

99.68  lbs.  steel @     8.5^  =  $8.47 

0.32  lb.  molybdenum @  $2.53   =        .81 

100.00  lbs.  alloy @     9.28^=   $9.28 

Excess  cost  in  manufacture  and  erection, 

say @     1.00^5=     1.00 


Total       =$10.28 


^=fF-- 


Working  tensile  stress  for  heat-treated  steel . . . .  =  38,000  lbs. 
Ditto  untreated  (assumed) =  30,000  lbs. 

Average  =  I  (2X30,000+38,000) =32,700  lbs. 

'  ■  -  •-  :.tSi 

.  ■■?■  'lev  ' 

CARBON    STEEL 

Working  tensile  stress  for  heat-treated  steel =  26,700  lbs. 

Ditto  untreated =  16,000  lbs. 

Average  =  ^  (2X16,000+26,700) =19,600  lbs. 

.     /     19,600     „  „  '      • 

..  r= — =  0.0 

32,700  ,rm 

'■  .  uh 

and  r/  =  l. 21X0. 6  =  0. 726 

As  this  is  far  lower  than  any  values  of  r  r'  given  in  Figs.  5a  and  56,  it 
is  evident  that  the  addition  of  molybdenum  to  carbon  steel  will  always 
effect  a  large  economy. 

ChroMol  Steel  versus  Chrome  Steel  ■'h&r.i. 

Referring  to  Tables  5a  and  56,  we  have  the  following: 

CHROMOL   steel 

98.93  lbs.  Steel '. @  8.5c^     ^$8.41 

0.76  lb.  Chromium @  25?^       ^      .  19 

0.31  lb.  Molybdenum @  $2.53   =      .78 

IflO.OOlbs.  Alloy. @    9.38cf  =  $9..38 


46  ECONOMICS   OF   BRIDGEWORK  Chapter  V 

CHROME   STEEL 

99  lbs.  Steel @  8.5ff  =$8.42 

1  lb.  Chromium. @  25^     =      .25 

100  lbs.  AUoy @  8.67^  =  $8.67 

....=-S.x.0S2 


CHROMOL    STEEL 

Working  tensile  stress  for  heat-treated  steel =  50,300  lbs. 

Ditto  untreated  (approximately) =  39,000  lbs. 

Average  =  ^  (2X39,000+50,300) =42,800  lbs. 

CHROME    STEEL 

Working  tensile  stress  for  heat-treated  steel =  46,300  lbs. 

Ditto  untreated  (assumed) =  33,000  lbs. 

Average  =  i  (2X33,000+46,300) =37,400  lbs. 

.     ,_37\400_ 

and  rr'  =  l. 082X0. 87  =  0. 94 

As  this  is  lower  than  nearly  all  the  values  of  r  r'  in  Figs.  5a  and  56,  it 
may  be  concluded  that  it  is  almost  always  economic  to  add  molybdenum  to 
chrome  steel;  or,  in  other  words,  chromol  steel  is  preferable  to  chrome 
steel  for  bridgework  on  account  of  both  cost  and  toughness. 

NiCMOL  Steel  versus  Nickel  Steel 

Unfortunately,  the  records  in  "Molybdenum  Commercial  Steels"  do 
not  give  any  tests  for  the  untreated  Nickel  Steel;  but  as  the  author  once 
made  some  tests  on  a  4 j%  nickel  steel  for  eye-bars,  he  will  use  the  results 
thereof  in  this  crude  investigation. 

Referring  to  Table  5/i,  and  employing  averages,  we  have  the  following: 

NICMOL  steel 

94.92  lbs.  Steel @  8.5^     =  $8.07 

4.50  lbs.  Nickel @  43^       =     1.94 

0.58  lb.  Molybdenum @  $2.53   =     1.47 


100.00  lbs.  Alloy @  11.48^  =  $11.48 


ECONOMICS   OF   ALLOY   STEELS  47 

Referring  to  Table  5g,  we  have 

NICKEL   STEEL 

96.00  lbs.  Steel @  8.5^     =  $8.16 

4.00  lbs.  Nickel @  43^       =     1.72 

100.00  lbs.  Alloy @  9.88^  =  $9.88 

.  .  r-1^-^^-1  162 


NICMOL   STEEL 

Working  tensile  stress  for  heat-treated  steel =  58,300  lbs. 

Ditto  untreated  (approximately) =  45,000  lbs. 

Average  =  i  (2X45,000+58,300) =49,400  lbs 

NICKEL   STEEL 

Working  tensile  stress  for  heat-treated  steel . . , .  =  40,000  lbs 

Ditto  untreated =28,000  lbs. 

Average  =  |  (2X28,000+40,000) =32,000  lbs. 

...  r'  =  ^^^  =  0.m 
49,400 

and  rr'=l. 162X0. 647  =  0. 752 

As  this  is  lower  than  any  of  the  values  of  r  r'  given  in  Figs.  5a  and  56, 
it  is  evident  that  the  addition  of  molybdenum  to  nickel  steel  will  always 
effect  a  large  economy. 

NicHROMOL  Steel  versus  Nichro  Steel 
Referring  to  Tables  5c  and  5d,  we  have  the  following: 

NICHROMOL   steel 

95.76  lbs.  Steel @  8.5^  =  $8.14 

0.86  1b.  Chromium @  25^  =  0.22 

2.95  lbs.  Nickel (^43^  =  1.27 

0 .43  lbs.  Molybdenum @  $2 .  53  =  1 .  09 

100.00  lbs.  Alloy @  10. 72)25  =  $10. 72 


48  ECONOMICS   or  BRIDGEWORK  Chapter  \' 

NICHRO    STEEL 

95.7  lbs.  Steel @  8.5^     =   S8.13 

1.0  1b.  Chromium @  25^       =     0.25 

3.3  lbs.  Nickel. @  43^       =     1 .42 

100.0  lbs.  Alloy @  9.8^     =   $9.80 

NICHROMOL   STEEL 

Working  tensile  stress  for  heat-treated  steel ....  =47,300  lbs. 

Ditto  untreated  (approximately) =  37,500  lbs. 

Average  =  i  (2X37,500+47,300) =40,800  lbs. 

NICHRO    STEEL 

Working  tensile  stress  for  heat-treated  steel  —  =  45,000  lbs. 

Ditto  untreated  (approximately) =35,500  lbs. 

Average  =  i  (2X35,500+45,000) =38,700  lbs. 

38,700^ 
40,800 

and  rr'  =  1.094X0. 949=  1.038 

Referring  to  Figs.  5a  and  56,  it  is  seen  that  the  simple-span  length  cor- 
responding to  this  product  is  about  600  feet  and  the  main  opening  for  a 
Type  A  cantilever  is  about  1,600  feet;  and  as  most  spans  are  below  this 
limit,  it  appears  probable  that  there  is  seldom  any  economy  in  adding 
molybdenum  to  chrome-nickel  steel  for  the  manufacture  of  bridges;  but 
the^data  used  for  this  investigation  are  so  crudely  approximate  that  this 
conclusion  requires  corroboration.  It  would  need  some  elaborate  and 
expensive  experimenting  to  determine  this  economic  point  with  accuracy. 
The  addition  of  the  molybdenum,  though,  would  undoubtedly  improve 
the  quality  of  the  alloy  by  increasing  its  resistance  to  shock. 

Chrovanmol  Steel  versus  Chrovan  Steel 
Referring  to  Tables  5e  and  5/,  we  have  the  following: 

chrovanmol  steel 

97.92  lbs.  Steel @  8.5^     =  $8.32 

1 .06  lbs.  Chromium (g).  25^       =  0 .  27 

0.17  lb.  Vanadium (a;,  $10.00=  1.70 

0.85  lb.  Molybdenum @  $2.53  =  2.15 

100. 00  lbs.  Alloy.... ■.;.......•. @  12.44^  =  $12.44 


J 


ECONOMICS   OF   ALLOY   STEELS  49 

CHROVAN  STEEL 

98.94  lbs.  Steel @  8.5^     =  $8.41 

0.90  1b.  Chromium @  25^       =     0.23 

0.16  1b.  Vanadium #$10.00=     1.60 


100.00  lbs.  Alloy %  10.24j^  =  $10.24 

•  r-^^^^-1215 

••'^"io:24-^-^^^ 


CHROVANMOL    STEEL 

Working  tensile  stress  for  heat-treated  steel  —  =63,300  lbs. 

Ditto  untreated  (entirely  assumed) =47,000  lbs. 

Average  =  I  (2X47,000+63,300) =  52,400  lbs. 

CHROVAN    STEEL 

Working  tensile  stress  for  heat-treated  steel . .  . .  =  56,000  lbs. 

Ditto  untreated  (entirely  assumed) =41,500  lbs, 

Average  =  |  (2X41,500+56,000) =46,300  lbs. 

and  rr'  =  1.215X0. 884  =  1.074 

From  Figs.  5a  and  56  we  find  that  this  product  corresponds  to  a  simple- 
span  length  of  about  750  feet  and  to  a  main  cantilever  opening  of  about 
2000  feet;  and,  as  these  are  excessive,  it  may  be  concluded,  for  bridgework, 
that  there  is  no  advantage  in  adding  molybdenum  to  chrovan  steel. 


The  next  economic  question  to  solve  is  that  of  the  gain  involved  by  in- 
creasing the  percentage  of  molybdenum  in  an  alloy  of  steel.  From  cer- 
tain diagrams  in  "Molybdenum  Commercial  Steels"  the  following  data 
for  comparison  of  chromol  steel  of  Classes  A  and  C  have  been  excerpted, 
the  treatment-temperature  being  800°  F, 

CLASS   A 

Average  analysis,  Carb.  0.15,  Mang.  0.38, 

Chrom.  0.72,  Moly.  0.28 

E.  L.  =  105,000  lbs.,  Ult.  =  130,000  lbs.,  Elong.  =  20%,  Red.  =  65%. 


50  ECONOMICS   OF   BRIDGEWORK  Chapteb  V 


CLASS    C 


Average  analysis,  Carb.  0.18,  Mang.  0.37, 

Chrom.  1.05,  Moly.,  0.73, 

E.  L.  =  150,000  lbs.,  Ult.  =  170,000  lbs.,  Elong.  =  18%,  Red.  =  58%. 


CLASS   A 


99:00  lbs.  Steel @  8.5jz^     =  S8.42 

0.72  1b.  Chromium @  25^       =     0.18 

0.28  lb.  Molybdenum @  $2.53  =     0.71 


100.00  lbs.  Alloy @  9.31^  =  $9.31 


CLASS    C 


98.22  lbs.  Steel @  8.5^^     =  $8.35 

1.05  lbs.  Chromium @,  2H       =     0.26 

0.73  lb.  Molybdenum @  $2.53  =     1.85 


100.00  lbs.  Alloy @  10.46^  =  110.46 

10.46     .   .„. 


CLASS   A 

Working  tensile  stress  for  heat-treated  steel  —  =43,300  lbs. 

Ditto  untreated  (assumed) =37,000  lbs. 

Average  =  i  (2X37,000+43,300) =39,100  lbs. 

CLASS    C 

Working  tensile  stress  for  heat-treated  steel  —  =  56,700  lbs. 

Ditto  untreated  (assumed) '. =48,500  lbs. 

Average  =  ^  (2X48,500+56,700) =  51,200  lbs. 

39,100^Q^g3 
51,200 

and  r/  =  1.124X0. 763  =  0. 858 

From  Figs.  5a  and  56  we  find  that  this  is  lower  than  those  recorded 
there  for  very  short  spans,  from  which  it  is  evident  that  increasing  the 
molybdenum  content  up  to  three  quarters  of  one  per  cent  is  in  the  line  of 
economy,  provided  that  the  resulting  alloy  be  not  too  brittle.  The  writer 
of  "Molybdenum  Commercial  Steels"  states  that  there  is  an  advantage 
in  using  molybdenum  up  to  a  limit  of  one  per  cent;  but  whether  this  can 


ECONOMICS   OF   ALLOY   STEELS 


51 


be  done  with  impunity  in  the  case  of  bridge  metal  can  only  be  proved  by 
actual  experiments  with  the  high  alloy  thus  produced. 


COMFILATION 


The  following  table  gives  a  resume  of  the  findings  and  deductions  herein 
evolved : 

TABLE   5m 


Kind  of  Steel 

Cost  per  Lb. 
in  Place 

Average  Intensity 
for  Tension 

Carmol 

9.28«f 

9.38^ 

11.48^ 

10.72^ 

12.44«f 

32,700  lbs. 
42,800  lbs. 
49,400  lbs. 
40,800  lbs. 
52,400  lbs. 

Chromol 

Nicmol 

Nichromol 

Chrovanmol 

An  inspection  of  Table  5m  shows  that  the  Carmol  and  Nichromol  steels 
are  out  of  the  running;  hence  it  will  be  necessary  to  test  the  three  others. 
Comparing  Chromoland  Nicmol,  we  have: 


11.48     42,800  _ 
'^'^~   9.38^49:400     ^"'^ 

From  Figs.  5a  and  56  we  find  that  this  product  corresponds  to  a  simple- 
span  length  of  about  700  feet  and  to  a  main  cantilever  opening  of  about 
1,900  feet,  hence  it  may  be  concluded  that,  except  for  unusually  long  spans, 
Nicmol  Steel  is  not  as  economic  as  Chromol  steel. 

Comparing  Chromol  and  Chrovanmol,  we  have: 

12^     42^800^ 
9.38    52,400 

As  in  the  last  case,  this  is  so  great  as  to  show  that  Chromol  steel  is  more 
economic  than  Chrovanmol  steel. 

From  all  that  precedes  it  is  evident  that  the  most  promising  combina- 
tion of  alloying  materials  for  a  high-grade  bridge-steel  is  one  of  chromium 
and  molybdenum;  and  a  good  analysis  to  test  as  a  starter  would  be  as 
follows: 

Carbon 0.25 

Manganese 0 .  75 

Chromium 0 .  75 

Molybdenum 0.75 


52 


ECONOMICS    OF   BRIDGEWORK 


Chapter  V 


It  would  not  do,  however,  to  confine  one's  attention  solely  to  Chromol 
steel  in  making  a  systematic  study  of  the  question  of  the  best  high-alloy 
of  steel  for  bridgework,  because  the  preceding  study  has  been  made  upon 
data  some  of  which,  of  necessity,  are  so  roughly  approximate  that  the 
findings  therefrom  have  to  be  taken  cum  grano  salts.  All  that  can  properly 
be  claimed  for  this  tentative  investigation  is  that  it  will  sei've  as  an  indi- 
cation that  an  exhaustive  series  of  tests  on  molybdenum  steel  for  bridges 
woidd  be  well  worth  while,  and  that  it  suggests  about  what  might  be 
expected  as  a  result  thereof. 


•  C   Jvii    D'iL'-' 


CHAPTER  VI 

COMPARATIVE   ECONOMICS   OF   BRIDGES   AND   TUNNELS 

The  contrasting  of  a  bridge  with  a  tunnel  or  a  combination  of  tunnels 
for  any  proposed  crossing,  in  respect  to  the  question  of  economics,  is  by  no 
means  easy;  because,  in  order  to  make  a  perfectly  just  comparison,  the 
facilities  afforded  by  the  two  structures  should  be  alike.  Generally,  lay- 
men make  the  mistake  of  pitting  a  single-track  tunnel  against  either  a 
double-track  bridge  or  a  purely  railway  tunnel  against  a  combined-rail- 
way-and-highway  bridge.  As  it  is  usually  uneconomic  to  make  the  interior 
diameter  of  a  tunnel  tube  much  greater  than  twenty  feet,  because  the  cost 
of  such  a  tube  increases  very  rapidly  with  the  diameter,  and  as  any  pro- 
jected bridge  that  is  in  competition  with  a  tunnel  is  necessarily  a  structure 
of  some  importance,  and,  therefore,  wide  of  deck,  it  is  evident  that  the 
comparison  will  probably  always  be  made  between  one  bridge  and  two  or 
more  tunnels.  Again,  as  the  travel  in  a  tube  of  twenty-foot  internal 
diameter  must  either  be  in  one  direction  only  or  else  very  slow,  two  tubes 
will  be  required  in  order  to  obtain  rapid  transit.  The  reason  for  this  is 
that,  in  a  tube  just  large  enough  for  two  lines  of  traffic  in  opposite  direc- 
tions, the  speed  is  absolutely  limited  to  that  of  the  most-slowly-moving 
vehicle;  because  it  would  be  impracticable  for  a  rapidly-moving  automobile 
to  turn  out  so  as  to  pass  a  slow  vehicle  without  facing  the  Hne  of  traffic 
coming  in  the  opposite  direction;  and  a  single  breakdown  would  quickly 
block  all  motion.  Anyone  who  gives  the  subject  any  thought  must  quickly 
arrive  at  the  conclusion  that  the  motion  of  traffic  in  any  highway-tunnel 
tube  must  be  restricted  to  one  direction  only.  ' 

Another  obstacle  to  the  satisfactory  comparison  of  these  fundamentally- 
different  types  of  transportation  structures  is  the  as-yet-unsolved  problem 
of  ventilation.  Many  engineers  contend  that  it  is  absolutely  unsafe  to 
run  automobiles  through  a  long  tunnel  because  of  the  exceedingly-poison- 
ous carbon-monoxide  given  forth  during  combustion;  while  others  say 
they  are  certain  that  such  traffic  can  be  maintained  without  danger. 
Probably  this  question  will  be  settled  finally  during  the  next  five  years, 
and  in  the  only  convincing  manner  possible,  viz.,  by  building  a  long  tunnel 
for  automobile  travel  and  operating  it.  As  it  is  stated  by  medical  men  of 
high  authority  that  the  action  of  carbon-monoxide  upon  the  human 
system  is  cumulative,  it  may  prove  difficult,  expensive,  or  even  totally 
impracticable  to  dilute  the  poison  to  such  an  extent  as  to  make  the  atmos- 

53 


54  ECONOMICS   OF   BRIDGEWORK  Chapter  VI 

phere  in  the  tube  perfectly  safe  for  breathing,  especially  by  people  of  feeble 
constitution. 

There  is  another  factor  that  is  likely  to  have  considerable  influence  in 
deciding  between  bridge  and  tunnel,  viz.,  that  driving  over  the  former  is 
much  more  agreeable  than  driving  through  the  latter.  Again,  walking 
through  a  long  tunnel  is  so  unpleasant  that  it  would  seldom  be  worth  while 
to  make  any  provision  whatsoever  for  pedestrian  travel  therein. 

Then,  too,  the  difference  between  the  height  of  climb  over  a  bridge  and 
the  depth  of  descent  into  a  tunnel  will  have  some  effect  upon  the  choice  of 
structure.  In  general,  it  may  be  stated  that  the  dip  of  a  tunnel  is  greater 
than  the  rise  of  a  low-level  bridge,  about  equal  to  that  of  an  ordinary  high-' 
level  bridge,  and  less  than  that  of  a  structure  below  which  pass  ocean-going 
vessels. 

Supposing,  however,  that  all  the  pros  and  cons  of  the  two  types,  barring 
cost  only,  about  balance  each  other,  the  question  for  settlement  would  be 
one  of  economics;  and  then  the  decision  would  favor  the  bridge,  because 
for  equal  facilities  the  cost  of  the  tunnel  almost  always  greatly  exceeds  that 
'of  the  bridge.  Of  course,  the  conditions  affecting  the  latter  might  be  so 
onerous  as  to  increase  the  cost  of  the  structure  beyond  any  reasonable 
limit — for  instance  a  span  of  unprecedented  length;  but,  in  general,  the 
bridge  costs  less  than  the  tunnel. 

In  the  author's  practice  he  has  twice  had  occasion  to  pit  bridge  against 
tunnel.  In  the  first  case  a  highway  suspension  bridge  with  a  span  of  1,750 
feet  and  a  total  clear  roadway,  including  sidewalks,  of  96  feet  was  con- 
trasted with  two  tubes  which  together  gave  a  clear  roadway  of  56  feet. 
The  result  was  that  the  tubes,  in  spite  of  their  smaller  carrying  capacity, 
cost  about  fifty  per  cent  more  than  the  bridge. 

In  the  other  case,  a  single-track-railway  tube  cost  considerably^  more 
than  a  double-track,  low-level  bridge — and  even  a  little  more  than  a  low- 
level,  combined-railway-and-highway,  double-deck  structure.  Comparing 
the  tunnel  and  a  high-level  bridge  with  a  clearance  above  high  water  of 
150  feet,  the  ratio  of  costs  of  a  two-tul)e,  railway  tunnel  and  a  double-track, 
railway  bridge  was  1.1;  and  comparing  a  three-tube  tunnel  for  both  railway 
and  highway  traffic  with  a  combined-railway-and-highway,  high-level 
bridge,  in  which  comparison  the  facilities  afforded  were  neai'ly  equal,  the 
ratio  of  costs  was  1.12 — both  of  these  results  being  in  favor  of  the  bridge. 

There  is  one  advantage  which,  theoretically,  the  tunnel  possesses  over 
the  bridge;  and  under  certain  conditions  it  might  become  i)racticall,y  opera- 
tive, viz.,  that,  while  a  wide-decked  bridge  has  to  be  built  all  at  once,  several 
tunnels  of  the  same  aggregate  width  can  be  constructed  from  time  to  time 
as  the  traffic  necessitates,  thus  saving  for  some  years  the  interest  on  the 
difference  between  first  costs. 

A  claim  has  been  made  that  any  bridge  having  more  than  about  forty 
feet  of  deck-width  will  congest  the  ti'affic  to  sucli  an  extent  that  there  is  no 
advantage  to  be  obtained  from  the  extra  width  above  the  said  forty  feet; 


COMPARATIVE    ECONOMICS    OF    BRIDGES    AND    TUNNELS  55 

but  such  an  idea  is  a  fallacy,  because  the  incoming  and  the  outgoing 
vehicles  could  enter  and  leave  the  bridge  at  points  two  blocks  apart,  and  a 
double-track,  electric-railway  line  could  enter  and  leave  by  the  street 
between.  If  this  arrangement  would  not  separate  the  incoming  and  the 
outgoing  traffic  sufficiently,  the  entrances  and  exits  might  be  located  four, 
six,  or  eight  blocks  apart — in  fact  there  need  be  no  restriction  as  to  the 
total  width  of  deck  in  case  that  this  method  of  traffic  separation  be  adopted. 

By  employing  a  spiral  approach  of  large  diameter,  the  traffic  could 
leave  the  periphery  thereof  at  three,  or  even  more,  points,  thus  making  the 
approaches  to  the  said  spiral  of  different  lengths,  but  all  comparatively 
short. 

Some  months  after  the  preceding  was  written  with  the  intention  of 
considering  the  treatment  of  the  subject  as  closed,  the  author  had  occasion 
to  prepare  for  the  American  Society  of  Civil  Engineers  a  paper  entitled 
"Bridge  versus  Tunnel  for  the  Proposed  Hudson  River  Crossing  at  New 
York  City";  and  as  it  gives  much  additional  information  upon  the  general 
economic  question  involved  in  this  chapter,  it  is  here  reproduced  practically 
verbatim: 

Whilst  making  lately  some  extensive  calculations  concerning  the  costs 
and  economics  of  long-span  suspension-bridges  for  his  forthcoming  treatise 
on  "Economics  of  Bridgework,"  the  author  has  had  occasion  to  figure 
weights  of  metal  for  a  number  of  such  spans;  and  by  means  of  the  result- 
ing data  he  was  able  to  undertake  an  investigation  of  the  comparative  costs 
and  efficiencies  of  bridges  and  tunnels  for  the  long-talked-of  crossing  of  the 
North  River  at  New  York  City.  Thinking  that  the  present  is  an  auspicious 
time  for  a  thorough  discussion  of  the  subject,  he  has  collected  and  condensed 
the  results  of  his  labors  and  incorporated  them  in  this  memoir  for  the 
Society. 

For  some  years  he  has  been  of  the  opinion  that  the  best  and  most 
economic  solution  of  the  problem  under  consideration  is  to  carry  all  street 
cars  and  subway  cars  beneath  the  water  and  the  strictly-highway  traffic 
above  it.  As  far  as  the  question  of  desirability  is  concerned,  this  arrange- 
ment would  be  the  best  practicable  for  the  following  reasons : 

First.  In  respect  to  cost  of  operation,  the  tunnel  would  require  a  dip 
of  ninety  feet  below  high-water,  and  the  bridge  a  rise  of  one  hundred  and 
eighty  feet  above  it;  consequently  it  is  evident  that,  as  far  as  the  matter 
of  expenditure  of  energy  is  concerned,  the  tunnel  would  be  decidedly  pref- 
erable. The  difference  in  cost  of  power  would  be  very  apparent  to  the 
management  of  the  electric  railways,  and  possibly  also  to  the  operators  of 
heavy  trucks,  but  it  would  not  be  noticed  at  aU  by  the  owners  of  automo- 
biles used  mainly  for  pleasure  traffic.  When  an  automobilist  is  about  to 
climb  a  long,  heavy  grade,  he  seldom  thinks  anything  concerning  how  much 
extra  his  gasoline  is  going  to  cost  him ;  but  the  officers  of  an  electric  railway 
line  generally  figure  with  the  greatest  of  care  on  the  item  of  power  expense, 
and  aim  to  reduce  it  to  a  minimum. 


56  ECONOMICS   OF   BRIDGEWORK  Chapter  VI 

Second.  In  regard  to  the  difference  in  the  expenditures  of  time  in  climb- 
ing up  and  down  the  approaches  of  the  two  crossings  under  comparison, 
the  gravity  of  this  matter  would  be  duly  appreciated  b}^  the  railroad  com- 
panj^  and  more  or  less  by  the  operators  of  ti-ucks,  but  it  would  not  be  recog- 
nized by  automobile  owners  and  users. 

Third.  As  to  the  agreeableness  of  the  two  kinds  of  crossing,  while 
people  do  not  particularly  fancy  going  under  ground  before  they  are  ulti- 
mately compelled  to,  they  soon  become  accustomed  to  passing  beneath  the 
water  in  electric  cars,  as  is  evidenced  by  the  many  New  York  business  men 
and  women  who  reside  on  Long  Island  or  in  New  Jersey.  Perhaps  in  time 
the  drivers  of  trucks  would  become  so  used  to  traversing  tunnels  as  not  to 
object  to  the  gloom  that  is  inherent  in  such  passage;  but  the  general  pub- 
lic, almost  to  a  man  (and  certainly  to  a  woman),  would  always  greatly 
prefer  driving  over  a  structure  that  provides  good  air  and  light,  and  usually 
a  fine  view  of  the  harbor  and  the  surrounding  country,  in  comparison  with 
traversing  a  long,  cramped,  and  dingy  tube. 

Fourth.  In  relation  to  the  question  of  sanitation,  there  is  practically 
no  greater  danger  to  health  in  passing  through  a  tunnel  in  which  the  power 
used  is  always  electrical  than  there  is  in  traversing  a  bridge;  but  the  safe 
ventilation  of  a  tube  carrying  automobile  traffic  is  as  yet  an  unsolved 
problem.  Figures  show  that  such  ventilation,  if  feasible,  would  be  exceed- 
ingly expensive,  and  the  velocity  of  the  passing  air  would  be  excessive. 

Again,  as  carbon  monoxide,  like  arsenic,  is  a  cumulative  poison,  there 
exists  a  possibility  that  the  regular  daily  passage  through  a  tube  where  the 
gas  remains  constantly,  even  in  minute  quantities,  would  eventually  under- 
mine one's  health.  Besides,  there  is  always  the  chance  of  a  blockade  of 
traffic  with  the  tunnel  full  of  automobiles,  and  these  may  be  counted  upon 
to  discharge  more  or  less  products  of  combustion  even  when  standing  still. 
Such  a  blockade  might  result  in  a  holocaust. 

The  author  sees  no  serious  objection,  however,  to  building  the  contem- 
plated highway  tunnels  under  the  North  River;  because  if,  after  comple- 
tion, they  prove  to  be  unsafe,  or  otherwise  unsatisfactory  for  automobile 
traffic,  they  can  either  be  used  by  electric  railway  cars  or  else  a  moving 
platform  can  be  put  in  to  carry  vehicles  through  A\'ithout  letting  them  use 
their  own  power.  The  experiment  of  automobile  transportation  through 
long  tunnels  might  be  worth  making,  for  the  results  in  any  event  would 
prove  of  great  interest  and  value  to  the  engineering  profession,  as  well  as 
to  the  general  public. 

In  making  the  comparative  estimates  of  cost  of  bridges  and  tunnels  for 
this  crossing,  the  author  adopted  four  (4)  per  cent  grades  on  the  approaches 
of  both  structures  and  clear  roadways  of  twenty-two  feet,  with  sidewalks 
eleven  feet  wide.  He  utilized  as  a  basis  for  his  comparison  the  cost  esti- 
mates for  tunnels  given  in  the  report  of  Clifford  M.  Holland,  M.  Am.  Soc. 
C.  K.,  Chief  Kiigineer  of  the  New  York  State  Bridge  and  Tinui(>l  Commis- 
sion and  the  New  Jersey  Interstate  Bridge  and  Tunnel  Conmiission;   but 


COMPARATIVE    ECONOMICS    OF    BRIDGES    AND    TUNNELS  57 

it  was  necessary  to  modify  some  of  the  items  for  the  increased  diameter  of 
tube  and  the  steeper  approach  grades,  also  to  omit  the  costs  of  equipment 
and  administration,  as  these  are  not  included  in  the  bridge  estimates.  For 
the  modification  of  cost  due  to  a  changed  diameter  of  tube,  it  was  assumed 
that  the  cost  per  lineal  foot  increases  and  decreases  as  the  square  of  the 
exterior  diameter.  This  assumption  is  almost  exactly  correct,  because  the 
thickness  of  the  shell  varies  directly  with  the  diameter,  as  does  also  the 
length  of  the  periphery,  consequently,  the  volume  of  the  shell  is  approxi- 
mately proportional  to  the  square  of  the  diameter.  Again,  the  volume  of 
excavation  for  any  shield-driven,  circular  tunnel  varies  as  the  square  of  the 
diameter;  and  as  almost  the  entire  cost  per  lineal  foot  is  that  of  the  shell 
plus  that  of  the  excavation,  it  is  evident  that  the  assumption  mentioned  is 
justified. 

Increasing  the  exterior  diameter  of  the  tube  to  thirty-one  (31)  feet 
makes  the  interior  diameter  twenty-seven  (27)  feet.  This  is  just  enough  to 
provide  a  clear  roadway  of  twenty-two  (22)  feet  in  the  highway  tunnel  and 
allows  just  enough  space  for  two  lines  of  the  widest  subway  cars  in  the 
electric-railway  tunnel. 

In  the  latter  type  it  is  feasible  to  contrast  the  cost  of  a  double-track 
tube  with  that  of  two  single-track  tubes;  but  in  a  highway  tunnel  it  is  not, 
because  a  breakdown  of  a  single  vehicle  would  block  all  traffic  until  it  is 
hauled  out  by  sending  a  double-ender  wrecking-car  into  the  tube  in  a 
reverse  direction  to  that  of  the  traffic.  With  such  an  occurrence  in  a 
double-track  tunnel,  the  automobiles  could  pass  by  the  wrecked  vehicle. 

If  there  were  an  accidental  stoppage  of  an  electric  railway  car  in  a 
single-track  tube,  it  would  cause  no  more  obstruction  to  rail  traffic  than  it 
would  if  the  accident  had  taken  place  in  a  double-track  tube  that  operates 
in  both  directions. 

The  author  computed  all  the  quantities  of  materials  in  substructure, 
superstructure,  and  approaches  of  six  structures,  in  order  to  plot  the  two 
cost  curves  for  bridges  shown  in  Fig.  6a.  On  that  diagram  are  given  the 
total  costs  for  bridges  with  their  approaches  and  for  timnels  with  their 
approaches  based  upon  the  unit  prices  which  governed  at  the  time  the 
tunnel  estimates  were  prepared.     The  principal  ones  of  these  are  as  follows: 

Wire  cables  in  place 23^  per  lb. 

Nickel  steel  in  place 11^  per  lb. 

Plain  concrete  in  shafts  and  anchorages     $16.00  per  cu.  yd. 
Mass  of  pneumatic  bases $35 .  00  per  cu.  yd. 

In  proportioning  the  substructures  the  author  made  the  dimensions  as 
small  as  considerations  of  true  efficiency  would  permit,  and  did  not  attempt 
any  beautification  of  structure  by  an  unnecessary  enlargement  of  piers.  If 
these  are  properly  built  to  meet  all  possible  conditions  of  loading  and  so  as 
to  provide  against  future  deterioration  caused  by  the  elements,  that  ought 
to  suffice;  and  so  doing  should  be  deemed  good  engineering  practice. 


58 


ECONOMICS   OF   BRIDGEWORK 


Chapter  VI 


In  order  to  make  the  investigation  general  instead  of  particular,  so  as 
to  apply  to  all  other  similar  river  crossings  by  verj'-high-level  suspension- 
bridges,  the  span-lengths  were  assumed  to  be  1,500,  2,300,  and  3,000  feet, 
to  permit  the  plotting  of  curves  of  total  costs  for  both  bridges  and  tunnels 
with  their  approaches  for  various  widths  of  river.  In  this  special  case  the 
span  length  would  have  to  be  about  2,900  feet;  and  in  all  cases  the  length 


1800      2000      2200      2400 
Mm  Spa/?  Len^f/>  ji)  feef. 

Fig.  6a.  Diagram  of  Total  Costs  of  Highway  and  Electric-Railway  Bridges  and 
Tunnels,  with  their  Approaches,  for  Crossings  Similar  to  that  of  the  North  River 
at  New  York  City. 

of  the  horizontal  portion  of  the  tunnel  has  been  assumed  to  be  exactly 
equal  to  that  of  the  main  span  of  the  competing  bridge. 

In  the  highway-structure  comparison  there  were  adopted  for  the  bridge 
three  clear  roadways  of  twenty-two  feet  each,  and  two  sidewalks  of  eleven 
feet  each,  corresponding  to  four  double-track  tubes  each  of  twenty-two 
feet  clear  roadway.     The  driveways  were  assumed  to  consist  of  creosotcd- 


COMPARATIVE    ECONOMICS    OP    BRIDGES    AND    TUNNELS  59 

wooden-block  pavement  supported  by  reinforced-concrete  slab,  and  the 
sidewalks  to  be  of  reinforced  granitoid. 

In  the  electric-railway-structure  comparison,  the  floors  were  assumed 
to  be  of  the  open  type,  having  wooden  ties  and  guardrails  and  the  usual 
steel  rails;  and  eight  lines  of  track  were  adopted  so  as  to  compare  with 
four  lines  of  double-track  tubes  and  with  eight  hues  of  single-track  tubes. 

In  every  possible  manner  the  comparison  was  made  fair  and  equitable, 
excepting  that  the  costs  of  right-of-way  and  property  damages  for  the 
approaches,  for  obvious  reasons,  had  to  be  ignored.  This  militated  against 
the  tunnel;  hence  in  any  actual  case  of  comparison  an  allowance  would 
have  to  be  made  for  the  difference  in  costs  of  right-of-way  and  property 
damages  for  the  approaches  to  the  two  structures.  In  the  case  of  the 
bridge,  by  purchasing  a  large  city-block  close  to  the  water  and  building  a 
spiral  approach  thereon,  the  cost  of  the  said  right-of-way  and  propertj^ 
damages  would  be  reduced  to  a  minimum;  and  even  that  cost  might  be 
offset  by  constructing  a  high  office  building  above  the  spiral.  Such  a 
building,  owing  to  its  location,  ought  to  possess  a  high  rental  value. 

Fig.  6a  shows  the  total  costs  of  main  span,  piers,  and  approaches  for 
both  highway  and  electric  railway  bridges  and  those  of  the  corresponding 
tunnels. 

As  before  indicated,  the  shortest  span-length  that  can  be  used  for  the 
proposed  North  River  bridge  is  about  2,900  feet,  for  which  length  the 
diagram  gives  approximately  the  following  costs: 

Highway  Bridge $32,500,000 

Four  Highway  Tunnels $49,000,000 

Electric-Railway  Bridge $34,500,000 

Four  Double-Track,  Electric-Railway  Tunnels. .  $48,000,000 
Eight  Single-Track,  Electric  Railway  Tunnels  . .  $30,000,000 

This  indicates  that  there  is  a  saving  of  cost  in  favor  of  the  highway 
bridge  amounting  to  $16,500,000,  and  one  of  $4,500,000,  in  favor  of  single- 
track,  electric-railway  tunnels.  The  former  saving  is  far  greater  than 
the  difference  in  costs  of  right-of-way  and  property  damages  for  bridge  and 
tunnel  is  ever  likely  to  be;  hence  the  conclusion  is  reached  that,  for  the 
proposed  North  River  crossing,  it  is  not  only  better  from  every  point  of 
view,  but  also  more  economic  to  carry  automobile  traffic  by  a  bridge  and 
electric  trains  by  single-track  tunnels. 

The  question  arises  as  to  how  cheaply  there  could  be  built  at  present 
prices  a  combination  of  bridge  and  tunnels  to  care  for  both  kinds  of  traffic. 
For  a  number  of  years  two  single-track  tubes  would  take  care  of  the 
electric-railway  trains,  hence  the  cost  would  be  as  follows: 

Highway  Bridge $32,500,000 

Two  Single-Track  Tunnels 7,500,000 

Total $40,000,000 


60  ECONOMICS   OF   BRIDGEWORK  Chapter  VI 

If  it  were  decided  that  a  bridge  having  a  total  width  of  roadways  of 
forty-fom-  (44)  feet  and  two  eleven-foot  sidewalks  inside  the  trusses,  would 
suffice  for  possible  future  conditions  of  traffic,  the  amount  of  money  re- 
quired for  the  combination  would  reduce  to  about  ^33,500,000. 

It  must  not  be  forgotten  that  these  totals  do  not  include  any  allowance 
for  right-of-way,  property  damages,  equipment,  or  administration. 

In  conclusion  the  author  offers  the  suggestion  that,  in  view  of  the  facts 
presented  in  this  memoir,  it  might  be  advisable  to  give  the  economics  of  the 
proposed  crossing  of  the  North  River  some  further  study  before  finally 
committing  the  community  to  the  policy  that  is  now  contemplated. 


The  preceding  paper  was  delivered  to  the  American  Society  of  Civil 
Engineers  in  May,  1920,  was  accepted  by  the  Publication  Committee, 
and  was  printed  immediately,  advance  copies  of  it  being  distributed  for 
discussion.  It  was  slated  for  delivery  at  the  meeting  of  September  third; 
but,  upon  very  short  notice,  its  reading  was  indefinitely  postponed.  The 
author  hopes  that,  in  the  interests  of  engineering  economics,  this  injunc- 
tion against  a  thorough  discussion  of  an  important  engineering  problem 
of  great  magnitude  will  not  prove  to  be  permanent. 


For  about  thirty  years  there  has  been  discussed  in  the  public  press  the 
proposed  construction  of  an  immense  bridge  across  the  North  River  to 
carry  all  kinds  of  traffic,  including  steam-railway  trains;  and  to-day  there 
is  serious  talk  of  materiahzing  the  project  by  building  for  that  purpose  a 
structure  to  cost  two  hundred  millions  of  dollars.  In  the  author's  opinion, 
the  construction  of  a  high  bridge  over  the  Hudson  at  New  York  City  for  the 
purpose  of  transferring  freight  and  passenger  trains  would  involve  a 
serious  economic  blunder  from  the  engineering  standpoint.  His  reasons 
for  this  rather  drastic  and  sweeping  statement  are  as  follows: 

First.  It  would  cost  more  to  build  at  this  location  a  standard  rail- 
way bridge  carrying  n  tracks  than  it  would  to  construct  /)  single-track 
tunnels. 

Second.  The  right-of-way  and  property  damages  would  be  much 
greater  for  a  railway  bridge  than  for  the  corresponding  tvmnels. 

Third.  The  cost  of  operation  to  cover  rise  and  fall  is  twice  as  great 
for  the  bridge  as  for  the  tunnels. 

While  the  unnecessary  expenditure  of  a  large  sum  of  money  for  the 
construction  of  the  proposed  bridge  might  bo  ]xirdoncd,  it  would  be 
exceedingly  uneconomic  to  saddle  for  centuiies  to  come  u]ion  posterity 
a  financial  burden  that  will  involve  needlessly  lifting  and  lowering 
ninety  feet  a  load  of  two  tons  for  each  ton  of  freight  carried  across  the 
river. 


CHAPTER  VII 

COMPARATIVE    ECONOMICS    OF   HIGH-LEVEL   AND   LOW-LEVEL    CROSSINGS 

The  term  high-level  is  applied  to  a  structure  having  all  its  spans  fixed 
and  its  deck  at  a  considerable  elevation  above  high-water  level;  but  the 
term  low-level  is  generally  interpreted  as  applying  to  structures  having 
one  or  more  movable  spans,  although,  strictly  speaking,  a  bridge  over  a 
non-navigable  stream  may  be  a  low-level  one  without  having  any  movable 
span. 

The  comparison  between  a  proposed  high-level  and  a  proposed  low- 
level  crossing  for  any  stream  is  generally  more  dependent  upon  the 
condition  of  expediency  than  it  is  upon  that  of  economy.  The  convenience 
of  the  passengers  is  often  the  criterion  that  will  settle  the  question;  but 
sometimes  convenience  has  to  be  ignored  because  of  the  paramount  con- 
dition of  first  cost.  Again,  the  comparison  will  depend  largely  upon  how 
much  higher  the  high-level  bridge  must  be  than  the  low-level  one,  and  upon 
the  height  and  slope  of  the  banks.  The  clear  channel  required  will  also  be 
of  some  importance,  the  wider  the  channel  the  greater  the  advantage  for 
the  high-level  bridge. 

Sometimes  in  a  long,  high-level  structure  with  only  one  channel  span 
required,  it  is  practicable  to  build  all  the  others  on  grade  and  as  deck 
spans,  economizing  on  substructure  and  shortening  the  approaches,  thus 
lowering  materially  the  total  cost  of  the  high-level  bridge. 

The  advantages  and  disadvantages  of  a  low-level  bridge  over  a  high- 
level  one  are  as  follows : 

Advantages 

a.  The  first  cost  is  almost  always  less. 

b.  The  costs  of  maintenance  and  repairs  are  less. 

c.  The  entrance  and  exit  are  closer  to  the  river. 

d.  The  chmb  is  less,  and,  therefore,  the  total  amount  of  power  of 

all  kinds  required  for  the  climb  is  less. 

e.  The  time  spent  in  crossing  is  less. 

Disadvantages 

/.      Increased  annual  expense  due  to  the  several  items  of  cost  in 
connection  with  operating  the  movable  span. 
61 


62  ECONOMICS   OF  BRIDGEWORK  Chapter  VII 

g.  Interruptions  to  travel  over  the  structure  from  opening  the 
movable  span. 

h.  A  somewhat  greater  obstruction  of  the  thoroughfare  in  respect 
to  vessel  traffic  as  well  as  to  the  passage  of  the  water,  in  case 
of  the  adoption  of  a  swing  span  with  its  protection. 

A  thorough  consideration  of  all  these  criteria  will  have  to  be  made 
before  a  logical  conclusion  can  be  reached  as  to  which  type  of  layout  is 
preferable. 

The  correct  ratio  of  first  costs  for  a  low-level  bridge  and  a  high-level  one 
of  the  same  capacity  and  strength  at  any  proposed  crossing  must,  of 
course,  be  determined  from  layouts,  computations  of  quantities  of  materials, 
and  estimates  based  upon  current  prices  of  the  said  materials  and  of  labor. 
It  is  sometimes  necessary,  however,  to  make  a  hurried  economic  compari- 
son; and  as  an  aid  in  so  doing  the  author  has  estabhshed  the  following 
results,  based  upon  assumed  conditions  that  may  properly  be  deemed  aver- 
age or  normal. 

Let  us  assume  a  double-track-railway  crossing  of  a  river  like  the  Mis- 
souri, requiring  1,500  feet  of  main  spans  with  a  vertical  clearance  of  50-feet 
above  high  water  for  passing  vessels,  a  variation  of  twenty-five  feet  be- 
tween extreme  stages  of  water,  a  horizontal  bed-rock  75  feet  below  high- 
water  elevation,  one  bank  high  and  sloping  back  from  high-water  line  at  a 
ratio  of  three  horizontal  to  one  vertical  and  the  other  bank  level  and  very 
low;  and  let  the  approach  grades  be  one  per  cent.  Under  such  condi- 
tions the  deepest  water  will  nearly  always  be  found  comparatively  close 
to  the  higher  bank,  and  the  position  of  channel  will  be  permanent;  conse- 
quently it  would  be  legitimate  to  employ  a  single  through  span  over  the 
second  opening  from  the  high-bank  end. 

With  certain  assumed  medium  unit  prices  for  materials  in  place,  the 
minimum  costs  of  these  two  structures  proved  to  be  as  follows : 

Low-Level  Bridge $1,204,000 

High-Level  Bridge $1,530,000 

The  ratio  of  these  costs  is  1.27 

With  a  low,  flat  approach  on  each  side,  and  the  other  conditions  un- 
changed, it  would  be  necessary  in  the  case  of  the  high-level  bridge  to  adopt 
a  level  grade  over  the  entire  river  so  as  to  provide  against  any  drastic  shift- 
ing of  channel;  and  in  the  case  of  the  low-level  bridge  to  figure  on  being 
able  to  take  down  the  towers,  machinery,  and  house  and  shift  them  to  any 
one  of  the  other  openings.  Under  these  conditions  the  costs  of  the  two 
structures  proved  to  be  as  follows: 

Low-Level  Bridge $1 ,256,000 

High-Level  Bridge $2,004,000 

The  ratio  of  these  costs  is  2.08 


ECONOMICS   OF   HIGH-LEVEL   AND    LOW-LEVEL   CROSSINGS         63 

For  one  of  the  author's  standard-type  highway-bridges,  having  four 
per  cent  grades  on  the  approaches  and  sand  foundations  at  a  depth  of  125 
feet  below  high  water,  the  other  conditions  being  as  previously  indicated 
for  the  crossing  with  one  high  and  one  low  bank,  the  estimated  costs  of 
structure  were  as  follows: 

Low-Level  Bridge $1,386,000 

High-Level  Bridge $1,371,000 

The  ratio  of  these  costs  is  0.99. 

For  the  layout  with  two  low  banks  the  costs  of  the  two  structures  were 
as  follows: 

Low-Level  Bridge $1,426,000  j 

High-Level  Bridge $1,623,000 

The  ratio  of  these  costs  is  1.14. 

The  main  reason  for  high-level  structures  costing  more  than  low-level 
ones  is  the  greater  lengths  and  costs  of  the  approaches;  and  as  in  highway 
bridges  the  grades  thereon  are  much  steeper  than  on  railway  bridges,  their 
ratios  of  costs  of  high-level  and  low-level  structures  are  less. 

It  will  be  necessary  to  compute  carefully  for  each  type  the  total  annual 
costs  of  maintenance,  repairs,  sinking  fund,  and  operation,  capitalize  these 
totals,  and  add  the  results  to  the  estimates  of  first  cost.  A  comparison  of 
these  sums  will  determine  the  financial  economics  of  the  two  types  com- 
pared. 

To  be  strictly  accurate,  however,  in  determining  these  comparing  figures, 
one  should  estimate  the  total  annual  costs  of  all  kinds  of  power  expended 
in  climbing  the  approaches,  capitalize  these,  and  add  them  to  the  previous 
sums  before  making  the  comparison;  but,  as  considerable  guess-work 
would  be  involved  in  making  such  a  computation,  it  might  be  exact  enough 
for  all  practical  purposes  to  assume  that  the  total  annual  costs  of  power 
are  the  same  for  the  two  types  of  structure. 


CHAPTER  VIII 

COMPARATIVE    ECONOMICS    OF    STEEL   AND    REINFORCED-CONCRETE 

STRUCTURES 

The  settlement  of  the  question  as  to  which  costs  more,  a  steel  bridge  or 
a  reinforced-concrete  one  of  the  same  capacity,  is  a  difficult  task.  For 
structures  of  ordinary  span-lengths,  under  normal  conditions  of  the  material 
market,  the  first  cost  of  the  steel  bridge  is  the  smaller,  but  when  the  price 
of  that  metal  takes  a  sudden  jump  the  reverse  is  true.  However,  in  a 
short  time  either  the  prices  of  concrete  materials  rise  to  correspond  or  else 
the  cost  of  the  metal  gradually  drops  back  until  a  normal  ratio  of  unit 
prices  for  bridge  materials  once  more  exists. 

But  the  question  of  the  economics  of  the  two  types  is  not  settled  by  a 
comparison  of  first  costs  alone,  because  the  elements  of  maintenance  and 
repairs  must  be  considered;  and  these  are  much  greater  for  the  steel 
structure  than  for  the  reinforced-concrete  one.  The  latter  requires  no 
painting,  and  there  should  be  no  renewal  of  parts  called  for,  excepting  only 
the  pavements,  while  in  the  former  these  items  are  often  large,  especially 
that  of  painting,  if  the  upkeep  be  properly  performed.  It  is  necessary, 
therefore,  to  capitalize  the  said  items  and  add  the  results  to  the  first  costs, 
in  which  case  under  normal  conditions  there  is  generally  but  little  differ- 
ence; and  as  the  painting  of  steel  structures  is  very  hkely  to  be  neglected 
and  the  metal,  in  consequence,  to  lose  its  normal  areas,  it  will  often  pay  to 
adopt  the  reinforced-concrete  construction,  even  when  the  economic  com- 
parison indicates  a  slight  disadvantage  by  so  doing. 

The  fact  that  the  annual  cost  of  maintenance  and  repairs  is  less  for 
reinforced-concrete  bridges  than  for  steel  ones  tends  to  render  the  former 
the  more  popular,  especially  amongst  those  persons  who  do  not  make  a 
practice  of  comparing  values  strictly  upon  the  basis  of  the  principles  of 
true  economy.  Such  persons,  too,  are  prone  to  say  that  the  reinforced- 
concrete  structure  is  superior  to  the  steel  one  because  of  its  longer  life, 
not  recognizing  the  facts  that  a  properly  designed,  built,  and  cared-for 
steel  bridge  will  do  its  work  for  a  very  long  term  of  years,  and  that  the 
longevity  of  reinforced-concrete  structures  as  yet  is  a  matter  of  surmise, 
in  view  of  the  uncertainty  about  the  efficiency  of  the  concrete  in  protect- 
ing the  reinforcing  steel  perpetually  against  rusting — which,  if  allowed  to 
continue,  will  c|uickly  and  inevitably  disintegrate  the  said  concrete  and 
destroy  the  structure. 

64 


ECONOMICS  OF  STEEL  AND  REINPORCED-CONCRETE  STRUCTURES         65 

The  comparison  of  the  types  is  complicated  also  by  the  matter  of 
personal  equation  in  designing;  for,  with  the  most  elaborate  and  rigid 
specifications  ever  written,  two  computers  working  independently  on  the 
same  job  would  be  likely  to  vary  in  their  final  results  far  more  in  reinforced- 
concrete  work  than  they  would  in  steelwork.  This  is  due  partially  to  the 
fact  that  the  science  of  reinforced-concrete  bridge  designing  is  newer  and 
less  highly  developed  than  that  of  proportioning  steel  bridges,  and  also 
because  in  the  former  type  equal  strength  can  be  secured  with  varying 
proportions  of  concrete  and  steel.  As  the  most  econqmical  proportions 
are  frequently  not  known,  it  is  evident  that  the  combined  costs  of  the  two 
materials  in  place  may  differ  appreciably.  Again,  in  arch  bridges  there  is 
often  a  choice  of  ratio  of  rise  to  span  or  even  of  span-lengths;  and  as  the 
effect  on  economics  by  variations  in  these  features  is  not  yet  determined 
with  accuracy,  the  final  estimates  of  cost  made  by  the  two  computers  are 
liable  to  be  still  more  widely  divergent  on  this  account. 

The  amount  of  attention  paid  to  aesthetics  when  making  the  design 
generally  affects  the  cost  of  a  concrete  bridge  more  than  it  does  that  of  a 
steel  one;  hence  this  factor  has  to  be  given  consideration  when  contrasting 
the  two  types  in  respect  to  the  matter  of  economics. 

The  size  of  the  live  load,  too,  is  likely  to  affect  the  comparison,  because 
a  diminution  thereof  cuts  down  the  cost  of  a  steel  structure  much  more 
than  it  does  that  of  a  concrete  one. 

For  short-span  bridges,  reinforced-concrete  has  an  advantage  over  steel 
in  respect  to  rigidity  of  structure;  and  under  certain  conditions  such  an 
advantage  may  be  of  importance,  but  ordinarily  it  is  not. 

There  is  another  complication  of  the  question,  which,  however,  ought 
not  to  be  allowed  to  exist,  viz.,  the  fact  that  many  small  reinforced-concrete 
bridges  are  designed  by  inexperienced  and  incompetent  computers,  who  are 
hired  by  municipalities  on  account  of  the  low  compensation  they  are 
wilHng  to  accept. 

Still  another  cause  for  divergence  is  the  great  variation  in  costs  of  exca- 
vation for  foundations  at  different  localities.  This  affects  the  substructure 
costs  for  reinforced-concrete  arch-bridges  far  more  than  it  does  those  for 
the  corresponding  steel  structures,  because  of  the  larger  footings  and  shafts 
of  the  former. 

Is  it  then  impracticable  for  a  bridge  engineer  to  settle  quickly  the  com- 
parative economics  of  the  two  types  of  construction  for  a  proposed  bridge? 
Not  at  all — only  it  will  take  more  time  than  that  required  for  the  deter- 
mination of  most  of  the  economic  problems  dealt  with  in  this  treatise.  The 
method  to  be  followed  is  this:  Having  obtained  in  advance  all  the  unit 
prices  for  materials,  figure  the  cost  of  the  steel  structure  by  means  of  the 
diagrams  of  quantities  given  in  Chapters  LV  and  LVI  of  "Bridge  Engineer- 
ing," then  find  that  for  the  reinforced-concrete  bridge  by  employing  the 
rules,  tables,  and  diagrams  given  for  that  purpose  in  the  latter  chapter, 
fixing  by  judgment,  whenever  necessary,  an  allowance  for  difference  in 


66  ECONOMICS    OF   BRIDGEWORK  Chapter  VIII 

costs  of  excavation.  As  explained  in  Chapter  XVII  of  this  work,  the  labor 
involved  in  making  such  computations  as  the  above-mentioned  is  by  no 
means  onerous. 

The  greater  the  span-lengths  which  are  necessitated  as  minimum  by  the 
conditions  of  the  crossing,  the  more  favorable  is  it  to  the  steel  structure 
in  the  economic  comparison;  and  when  a  certain  span-length  has  been 
reached,  the  reinforced-concrete  structure  becomes  impracticable.  What 
this  limiting  span-length  is,  designers  have  not  yet  determined  with  gen- 
eral satisfaction;  but  the  author  is  of  the  opinion  that  it  is  not  very  far 
from  seventy  (70)  feet  for  girders  and  three  hundred  (300)  feet  for  arches. 
While  it  is  practicable  to  build  reinforced-concrete  arch-spans  of  greater 
length  than  the  latter  figure,  much  trouble  would  be  involved  during  their 
erection  by  the  unequal  and  abnormally  great  settlement  of  the  falsework, 
which  settlement  tends  to  distort  the  arch  rings  and,  in  consequence,  to 
give  the  structure  an  unsightly  appearance.  Such  settlement  can  be 
reduced,  if  sufficient  care  be  taken;  but  an  excessive  amount  of  the  latter 
adds  to  the  time  required  for  fieldwork  and,  consequently,  to  the  first  cost. 

In  general,  it  may  be  stated  that  a  high-level  crossing  is  usually 
more  favorable  to  a  steel  structure  than  to  one  of  reinforced-concrete,  as 
are  likewise  deep  foundations  and  perilous  erection  conditions;  also  that, 
other  things  being  equal,  a  great  width  of  deck  generally  militates  in  favor 
of  the  reinforced-concrete  type  of  construction;  as  do,  too,  the  remoteness 
of  the  site  from  the  source  of  the  structural-steel  supply  and  the  cheapness 
of  common  labor  available  for  fieldwork. 

It  may  be  that  some  reader  of  this  chapter  wiU  claim  that  it  is  rather 
indefinite  in  its  conclusions  and  deals  mainly  with  glittering  generalities. 
Possibly  there  may  be  some  justice  in  such  a  claim;  but  it  must  not  be 
forgotten  that  the  economics  of  the  two  contrasted  types  of  bridges  is 
primarily  dependent  upon  such  arbitrary  and  uncertain  conditions  as  the 
relative  prices  of  steel  and  cement,  the  availability  of  concrete  aggregate, 
the  comparative  costs  of  high-grade  and  low-grade  labor,  and  the  distances 
of  the  bridge  site  from  the  various  sources  of  supplies.  This  fact  makes  it 
impossible  to  come  to  any  fixed  or  reliable  conclusion  concerning  the 
relative  economics  of  steel  and  reinforced-concrete  bridges. 


CHAPTER  IX 

COMPARATIVE    ECONOMICS    OF    DIFFERENT    TYPES    OF    ORDINARY    STEEL 

STRUCTURES 

Under  the  term  ordinary  steel  structures  will  be  included  only  girder 
or  simple-truss  fixed  spans  of  the  following  types: 

Deck,  rolled-T-beam  spans. 

Deck,  plate-girder  spans. 

Half-through,  plate-girder  spans. 

Deck,  open-webbed,  riveted  spans. 

Through,  riveted  spans. 

Deck,  pin-connected  spans. 

Through,  pin-connected  spans. 
The  economics  of  all  other  types  of  steel  bridges  will  be  treated  in 
other  chapters. 

ROLLED-I-BEAM    SPANS 

These  are  always  deck  structures  because  of  the  shortness  of  their 
limiting  lengths.  They  are  preferable  to  plate-girder  bridges  up  to  the 
limit  which  due  consideration  for  the  question  of  deflection  sets,  even  if  the 
economic  Hmit  for  weight  of  metal  be  exceeded.  This  is  because  of  their 
extreme  simpUcity  for  both  manufacture  and  erection,  and  also  at  most 
times  because  the  base  prices  for  rolled  I-beams  are  lower  than  those  for 
plates  and  light  shapes — besides  the  cost  of  shopwork  is  less,  owing  to  the 
small  amount  of  detaihng  and  the  comparatively  few  rivets  that  have  to 
be  driven.  In  respect  to  the  economics  of  erection,  they  are  generally  built 
of  standard  lengths  and  sizes,  thus  permitting  the  larger  railroad  systems 
to  keep  a  supply  of  them  in  stock  to  be  used  for  emergencies.  Moreover, 
they  are  put  in  place  very  readily,  and  there  are  but  few  rivets  to  drive. 
Of  course,  plate-girder  spans  could  be  standardized  and  employed  in  the 
same  manner,  but  not  quite  so  conveniently. 

For  ordinary  I-beams  the  longest  steam-railway  spans  are  about  twenty 
(20)  feet  when  four  lines  of  stringers  per  track  are  adopted,  but  by  employ- 
ing the  thirty  (30)  inch  special  sections  of  the  Bethlehem  Steel  Company 
the  hmit  can  be  increased  to  about  thirty  (30)  feet  for  fairly-heavy  engine- 
loads.  By  using  six  lines  of  beams  per  track  the  limit  can  be  increased 
to  about  thirty-five  (35)  feet,  for  which  span  the  depth  is  only  one-four- 
teenth (1/14)  of  the  length,  a  ratio  common  enough  in  England,  but  ob- 

67 


68  ECONOMICS    OF   BRIDGEWORK  Chapter  IX 

jected  to  by  most  American  railway  engineers  on  account  of  the  great  de- 
flection that  it  permits. 

Deck  Plate-Girder  Spans 

Although  plate-girders  are  of  necessity  as  unscientific  structures  as  a 
bridge  specialist  ever  has  to  design,  they  are  without  doubt  the  most  satis- 
factory type  of  construction  possible  for  short  spans.  Their  superiority 
over  articulated  trusses  is  due  to  the  following  reasons: 

First.  OAving  to  their  compactness  they  better  resist  shock  and  check 
vibration. 

Second.  They  have  fewer  critical  points  where  overstress  is  hkely  to 
exist  because  of  faults  of  either  designing  or  workmanship. 

Third.  A  number  of  loose  rivets  lying  close  together  will  do  far  less 
harm  in  a  plate-girder  than  in  an  open-webbed  one. 

Fourth.     The  cost  of  manufacture  per  pound  of  metal  is  a  little  less. 

Fifth.  Owing  to  the  steady  demand  for  plate-girder  structures  and 
the  comparatively  small  number  of  the  sections  of  metal  used  in 
their  manufacture,  it  is  easy  to  obtain  quickly  the  materials  required; 
and  the  work  on  the  metal  is  of  a  simple  character.  For  these  reasons 
plate-girder  spans  can  generally  be  purchased  with  less  delay  than  open- 
webbed  girders. 

Sixth.  The  cost  per  pound  for  erection  is  decidedly  less,  excepting 
where  the  conditions  are  unusual,  and  the  cost  of  painting  is  comparatively 
small. 

Seventh.  They  can  be  overstressed  without  danger  much  higher 
than  open-webbed  girders. 

Eighth.  They  are  less  liable  to  injury  by  accident  than  articulated 
trusses. 

Ninth.  They  are  more  easily  painted,  and  are  more  accessible  to 
examination  for  rust. 

Tenth.  The  cost  of  maintenance  is  less,  owing  to  the  absence  of  small 
parts  and  details  that  might  work  loose  under  traffic. 

The  ordinary  limit  of  length  of  plate-girder  spans  is  about  one  hundred 
(100)  feet,  but  that  limit  has  often  l)een  surpassed  by  twenty-five  (25)  or 
thirty  (30)  per  cent  for  simple  spans  and  by  much  more  for  swing  spans. 
Usually  it  is  the  difficulty  in  shipping  very  long  plate-girders  from  bridge 
shop  to  site  that  determines  the  superior  limit  of  such  spans.  The  loading 
of  long  girders  on  cars  for  shipment  is  quite  an  art,  and  it  should  be  en- 
trusted only  to  men  experienced  in  such  loadings;  for,  otherwise,  the  metal 
is  liable  to  be  injured  in  transit  or  the  cars  to  break  down,  or  some  other 
trouble  is  likely  to  happen  befoi-e  they  reach  their  destination.  Some  en- 
gineers believe  that  the  liability  to  injury  of  long  plate-girders  in  shop, 
transit,  and  field  should  limit  their  loiigtli  to  one  Innidred  (100)  feet;  but 
the  author  is  not  of  this  opinion,  foi-  he  thinks  that  by  taking  jiroper  pre- 


ECONOMICS  OF  DIFFERENT  TYPES  OF  ORDINARY  STEEL  STRUCTURES       69 

cautions  the  danger  can  be  pretty  nearly  eliminated.  About  as  long  a 
plate-girder  as  has  ever  been  shipped  in  one  piece  was  one  of  one  hundred 
and  thirty-two  (132)  feet.  It  required  four  flat-cars  to  transport  it. 
Longer  plate-girder  spans  than  this  have  been  built,  notably  tubular 
bridges  and  swing  spans,  but  they  were  shipped  in  parts  and  assembled 
at  site.  This  expedient  for  simple  spans  is  really  permissible  only  in  case 
of  bridges  to  be  sent  to  foreign  countries,  and  it  is  to  be  avoided  if  possible 
even  then,  because  it  is  sometimes  difficult  to  obtain  a  satisfactory  job  of 
field-riveting  when  making  the  splices,  although  the  use  of  pneumatic 
riveters  tends  to  reduce  materially  the  force  of  this  objection. 

As  far  as  economics  is  concerned,  it  may  be  stated  that,  if  deck  plate- 
girders  are  feasible  for  any  opening,  they  are  more  economical  than  truss 
spans  up  to  a  length  that  is  prohibitory  for  shipment.  As  the  depth  of  a 
very  long  plate-girder  is  generally  from  one-tenth  (1/10)  to  one- twelfth 
(1/12)  of  the  span,  the  requirements  of  underneath  clearance  often  bar 
out  deck  plate-girders  and  necessitate  either  half -through  plate-girders  or 
through  trusses. 

Again,  the  great  depth  required  for  very  long  plate-girder  spans  often 
sets  the  limit  for  span-length  because  of  shipping  requirements.  Some 
railroads  have  tunnels  and  overhead  crossings  which  are  lower  than  cus- 
tom is  now  requiring;  and  very  deep  girders  loaded  on  flat-cars  might  not 
be  able  to  pass — nor  could  such  girders  be  placed  flat,  because  then  the 
horizontal  clearance  would  be  encroached  upon. 

Half-Through  Plate  Girder-Spans 

The  economic  limit  of  length  for  this  type  of  structure  is  materially 
less  than  that  of  the  type  just  treated,  because  of  the  necessity  for  using  a 
steel  floor.  On  this  account  it  has  not  the  advantage  over  the  through- 
truss  bridge  which  the  deck-plate  girder  structure  possesses.  For  a  length 
of  one  hundred  (100)  feet  the  weight  of  metal  in  the  latter  type  exceeds 
that  in  the  former,  by  from  five  (5)  to  fifteen  (15)  per  cent,  the  smaller  figure 
being  for  the  lightest  live-loads  and  the  larger  for  the  heaviest.  Of  course, 
the  cheaper  metal  of  the  plate-girder  type  would  tend  to  offset  its  greater 
weight,  but,  in  order  to  make  the  costs  of  the  two  100-ft.  steam-railway- 
bridge  spans  the  same,  the  ratio  of  pound  prices  for  metal  erected  in  the 
girders  and  trusses  themselves  would  have  to  be  from  1.1  to  1.3 — a  condi- 
tion of  market  that  is  unusual.  But  as,  for  various  good  reasons,  it  hardly 
seems  advisable  to  build  through,  steam-railway  spans  shorter  than  one 
hundred  (100)  feet,  it  is  well  to  adopt  this  length  as  the  superior  limit  for 
half-through  plate-girders  and  deck  plate-girders  in  standard  railway 
bridges.  For  electric-railway  bridges  and  highway  bridges,  this  limit 
might  advantageously  be  reduced  to  about  seventy-five  (75)  feet. 


70  ECONOMICS   OF   BRIDGEWORK  Chapter  IX 


Deck,  Open-Webbed,  Riveted  Spans 

Some  engineers  entertain  the  notion  that  for  short  deck-spans  an  econ- 
omy can  be  effected  by  using  open-webbed  girders  instead  of  plate-girders. 
If  there  be  no  objection  to  increasing  the  depth  considerably,  some  metal 
can  be  saved  in  this  way;  but,  if  the  same  depth  must  be  employed  for 
both  types,  there  is  but  httle,  if  any,  saving  in  weight,  provided  that  the 
detaihng  be  done  properly — besides  the  pound  price  of  the  manufactured 
steel  is  a  trifle  greater  for  the  open-webbed  structure. 

Some  years  ago  there  were  designed  for  a  transcontinental  Une  a  number 
of  plate-lattice-girder  spans.  Their  raison  d'etre  was  supposed  to  be 
primarily  their  ability  to  pass  water  through  them  when  submerged,  but 
secondarily,  economy.  The  designer  claimed  that  they  effected  a  saving 
of  metal  amounting  to  about  fifteen  hundred  (1500)  pounds  for  an  eighty 
(80)  foot,  single-track  span,  and  that  the  pound  price  for  their  manufac- 
ture was  no  greater  than  that  for  ordinary  plate-girder  work.  The  author 
once  used  plate-lattice  girders  for  the  cross-girders  of  the  Union  Loop 
Elevated  Railroad  of  Chicago,  but  his  object  was  simply  to  evade  a  trouble- 
some clause  in  the  city  ordinance.  The  webs  of  these  cross-girders  were 
solid  near  mid-span  and  at  the  ends,  and  were  open  near  the  quarter  points, 
while  those  of  the  railroad  girders  previously  mentioned  were  sohd  at  the 
ends  and  open  over  more  than  the  middle  half  of  the  total  length.  As 
far  as  the  author's  experience  goes,  it  takes  just  as  much  metal  to  build  the 
webs  open,  and  the  pound  price  for  the  finished  metal  is  a  trifle  greater 
than  it  is  for  ordinary  plate-girder  construction.  The  fact  that  this  same 
railroad,  when  drawing  up  a  set  of  standard  plans  a  few  years  later,  dis- 
carded the  plate-lattice  girders  is  a  pretty  sure  indication  that  the  advan- 
tages claimed  for  them  were  more  imaginary  than  real.  It  is  true,  of  course, 
that  in  case  of  submergence  they  would  pass  a  certain  amount  of  water 
through  their  webs;  but  it  is  seldom  that  a  railroad  company  will  build 
a  bridge  of  any  kind  so  close  to  the  high-water  mark  as  to  run  any  risk  of 
its  being  submerged. 

In  respect  to  the  economics  of  deck  and  through  riveted  spans,  it  may 
be  stated  as  a  general  proposition  that,  although  the  former  sometimes 
require  more  metal  than  the  latter,  they  effect  a  great  saving  in  the  cost  of 
the  piers,  and  hence  are  to  be  adopted  whenever  permissible.  Deck  spans 
are  cheaper  per  se  when  the  ties  can  rest  on  the  chords.  This  arrangement 
works  well  with  double-track  bridges  having  trusses  spaced  about  twenty 
feet  centers  with  two  lines  of  stringers. 

The  question  of  the  comparative  economics  of  pin-connected  and  riveted 
spans  is  treated  at  length  in  the  next  chapter. 

In  respect  to  the  comparative  economics  of  the  various  kinds  of  trusses, 
it  might  be  stated  that  a  very  few  of  them  have  stood  the  test  of  time,  all 
freak  and  expensive  styles  having  been  discarded,  the  only  types  used 


ECONOMICS  OF  DIFFERENT  TYPES  OF  ORDINARY  STEEL  STRUCTURES       71 

today  being  the  Pratt,  Petit,  Triangular  (both  simple  and  sub-divided  and 
including  the  Warren),  and  K  trusses. 

Comparing  Pratt  and  Petit  truss-spans,  for  which  there  is  no  difference 
worth  mentioning  in  the  pound  prices  of  the  metal,  the  weights  per  foot  (and 
therefore  the  costs)  are  alike  for  single-track  spans  of  three  hundred  (300) 
feet,  and  for  double-track  spans  of  three  hundred  and  fifty  (350)  feet;  but 
both  constructive  and  aesthetic  reasons  generally  necessitate  limiting  the 
lengths  of  Pratt  trusses  to  about  three  hundred  and  twenty-five  (325) 
feet. 

In  respect  to  the  comparative  economics  of  the  Pratt  and  Triangular 
trusses,  there  seems  to  be  a  difference  of  opinion  amongst  bridge  engineers. 
The  author  has  found  very  little  variation  in  their  total  weights  of  metal, 
with  occasionally  a  slight  economy  in  favor  of  the  Triangular  truss. 
That  truss  has  the  practical  advantage  that  changes  in  chord  stresses 
occur  at  only  every  other  panel  point.  This  often  makes  it  possible 
to  section  the  chords  more  economically. 

As  explained  at  length  in  Chapter  XI,  for  continuous  trusses  of  very 
long  span,  the  Triangular  truss  has  quite  an  advantage  over  the  Petit 
truss. 

The  K  truss  is  appUcable  for  long  spans  only,  and,  therefore,  is  in  com- 
petition with  the  Petit  truss  and  not  with  the  Pratt.  Its  principal  claim 
for  economy  lies  in  ease  and  simplicity  of  erection,  but  it  also  has  a  tendency 
to  reduce  the  high  secondary  stresses  inherent  in  the  Petit  type.  It  was 
employed  to  advantage  in  the  design  of  the  great  Quebec  cantilever  bridge. 

The  statements  made  in  this  chapter  apply  mainly  to  railway  bridges 
and  heavy  highway  structures.  For  light  highway  bridges  some  of  them 
might  require  a  slight  modification. 


CHAPTER  X 

COMPARATIVE    ECONOMICS    OF   RIVETED   AND   PIN-CONNECTED    BRIDGES 

For  at  least  a  dozen  years  near  the  close  of  the  last  century  there  was 
waged  in  the  technical  press  and  orally  when  bridge  engineers  met  (espe- 
cially if  there  were  both  Europeans  and  Americans  present)  a  war  of  words 
concerning  the  relative  merits  of  riveted  and  pin-connected  bridges;  but 
all  arguments  that  were  advanced  failed  to  solve  the  disputed  question. 
Time  and  the  steady  development  of  the  real  science  of  bridge  designing, 
however,  gradually  brought  about  changes  of  opinion  among  the  leaders 
in  that  specialty;  and  the  matter  was  finally  settled  upon  a  compromise 
basis. 

The  advocates  of  riveted  structures  used  to  claim  greater  rigidity  and 
an  increased  chance  for  safe  passage  by  a  derailed  train,  while  the  endorsers 
of  pin-connected  construction  used  to  rest  their  case  mainly  upon  the  theo- 
retically-correct distribution  of  stresses  by  articulated  joints  and  the 
smaller  amount  of  metal  needed  for  building.  It  is  true  that  there  was  then 
a  wide  divergence  in  the  weights  of  metal  required  for  constructing  riveted 
and  pin-connected  bridges  to  carry  the  same  Uve  loads;  and  for  this  there 
were  two  saUent  reasons.  First,  the  riveted  structures  were  of  the  lattice- 
girder  type,  having  two,  three,  or  even  four  systems  of  triangulation,  thus 
involving  much  idle  or  superfluous  metal  in  the  main  members  of  the  web 
and  even  more  in  the  numerous  connecting  plates  and  fillers;  and,  second, 
the  pin-connected  structures  were  proportioned  essentially  for  the  theo- 
retical stress-requirements,  irrespective  of  proper  minimum  sections,  thus 
cutting  the  weight  of  metal  down  to  an  absolute  minimum. 

Gradually,  though,  these  two  types  approached  each  other  in  weight, 
the  lattice-trusses  being  abandoned  for  the  riveted  single-intersection  types, 
such  as  the  Warren  and  the  Pratt,  and  experience  in  operation  showing  in 
pin-connected  trusses  the  necessity  for  stiffening  the  abnormally-light 
members  so  as  to  increase  the  rigidity  and  check  the  vibration.  Today 
good  designers  of  riveted  structures  intersect  all  the  axial  lines  of  main 
members  at  panel  points  just  as  carefully  as  do  the  designers  of  pin-con- 
nected structures;  and,  hence,  the  prime  objection  to  the  former  type, 
viz.,  its  unscientific  intersection  of  symmetry  lines,  vanishes  in  ioto.  It  is 
true,  though,  that  there  remain  the  unavoidable  secondary  stresses,  but 
these  exist  also  to  a  small  degree  in  pin-connected  bridges  because  of  the 
friction  of  the  pins  in  their  holes  and  the  consequent  failure  of  the  joints  to 
function  as  actual  articulations.     The  employment  of  eye-bars  certainly, 

72 


ECONOMICS   OF  RIVETED   AND    PIN-CONNECTED   BRIDGES  73 

cuts  down  the  quantity  of  metal,  because,  in  the  members  where  they  are 
used,  the  weight  of  steel  for  both  main  sections  and  details  is  an  absolute 
minimum;  and,  in  general,  pins  weigh  less  than  connecting  plates.  Whether 
secondary  stresses  receive  proper  consideration  or  not,  a  pin-connected 
bridge  is  somewhat  lighter  than  the  corresponding  riveted  one,  and  there- 
fore ought  to  be  less  expensive.  It  is  true  that  the  fine  shopwork  requisite 
for  the  proper  manufacture  of  pins  and  for  the  drilling  of  pin-holes  makes 
the  pound  price  for  fabrication  greater  in  the  pin-connected  structure;  but 
this  is  offset  more  or  less  by  its  lower  pound  cost  for  erection,  owing  to  the 
smaller  number  of  field  rivets  to  be  driven,  the  shorter  time  required  to 
make  safe  against  loss  of  span  by  washout  of  falsework,  and  the  reduction 
in  overhead  expense  effected  by  minimizing  the  time  for  field  operations. 

From  a  study  of  the  diagrams  of  weights  of  metal  per  lineal  foot  of 
span  for  pin-connected  and  riveted-truss  bridges  given  in  Chapter  LV 
of  "  Bridge  Engineering,"  it  is  found  that  the  weights  of  the  latter 
exceed  those  of  the  former  by  the  following  percentages: 


Simple  Spans 

Span  Lengths 
200' 

Percentage  of  Increase 
4 

300' 

5 

400' 

6 

500' 

8 

600' 

11 

700' 

14 

Cantilever  Spans 

Main  Openings 
600' 

Percentage  of  Increase 
6 

1000' 

9 

1400' 

13 

It  is  seen  from  these  tables  that  the  percentage  of  saving  by  using  pin- 
connections  increases  gradually  with  the  span-length.  This  is  because  of 
the  effect  of  the  reduced  dead-loads. 

Notwithstanding  the  fact  that  pin-connected-truss  bridges  are  some- 
what fighter,  and  possibly  somewhat  cheaper,  than  the  corresponding 
riveted-truss  bridges,  the  latter  are  decidedly  preferable  for  all  short  or 
medium-length  spans  of  railway  structures  (both  steam  and  electric); 
because  in  short,  pin-connected  spans  the  vibration  from  rapidly-passing 
loads  is  so  great  that  the  motion  of  the  eyes  on  the  pins  causes  such  a  grind- 
ing of  both  that  eventually  the  structure  has  to  be  replaced  on  that  account. 
This  was  shown  long  ago  to  be  the  case  in  pin-connected  elevated  railroads; 
and  lately  it  has  been  found  necessary  to  replace  pins  in  a  number  of  rail- 


74  ECONOMICS   OF  BKIDGEWORK  Chapter  X 

road  bridges.  The  author  saw  an  elevated  raUroad  in  Kansas  City  re- 
moved practically  for  this  cause  alone,  the  pins  having  been  cut  into  and 
the  eyes  elongated  as  much  as  an  eighth  of  an  inch.  In  the  author's 
opinion,  a  steam-railroad-bridge  span  should  be  pretty  long  before  pin- 
connections  are  resorted  to — say  500  feet  for  simple  spans  and  900  feet  for 
the  main  openings  of  cantilevers;  but  for  highway  and  electric-railway 
bridges  these  lengths  may  be  cut  down  from  twenty-five  to  thirty-five 
per  cent.  The  point  is  one  to  be  settled  by  individual  judgment  based  upon 
experience — not  prejudice.  The  size  of  the  appropriation  available  for 
construction  may  quite  legitimately  be  a  ruhng  factor  in  making  the  deci- 
sion, because  a  pin-connected  highway  span  of  five  hundred,  or  even  four 
hundred  feet,  does  not  make  a  bad  bridge;  although,  if  the  traffic  be  great, 
such  a  structure  certainly  is  inferior  to  a  riveted  one,  in  that  it  will  vibrate 
more  and  will  possibly  be  shorter  hved.  But  if  the  Uve  load  assumed  for 
the  designing  be  never  greatly  exceeded,  and  if  the  structure  be  always  kept 
properly  painted,  it  would  probably  require  more  than  a  century  of  use  to 
wear  the  pins  and  pin  holes  to  any  dangerous  extent. 

The  discovery  of  a  high-alloy  of  steel  that  can  be  manufactured  at  rea- 
sonable cost,  and  the  development  of  a  satisfactory  and  absolutely-rehable 
method  of  heat  treatment  thereof  for  eye-bars  may  bring  the  pin-connected 
structure  once  more  into  vogue;  but  it  will  be  for  long  spans  only,  and 
preferably  for  highway  structures. 


CHAPTER  XI 

COMPARATIVE    ECONOMICS   OF   CONTESTUOUS   AND    NON-CONTINUOUS  TRUSSES 

This  chapter  is  mainly  a  reproduction  of  a  joint  paper  by  Mr.  H.  Mal- 
colm Priest  and  the  author,  lately  presented  to  the  Engineers'  Society  of 
Western  Pennsylvania. 

For  many  years  past  bridge  engineers  have  held  differing  opinions  con- 
cerning the  advantages  of  continuous  trusses  as  compared  with  the  cor- 
responding non-continuous  ones.  Some  claimed  a  great  saving  in  weight 
of  metal  from  continuity  while  others  felt  sure  there  was  none.  The  author 
had  been  under  the  impression  that  the  advantage  claimed  for  the  contin- 
uous truss  was  mainly  due  to  the  ignoring  of  the  effect  of  reversing  stresses; 
and,  as  will  be  seen  later,  in  this  opinion  he  was  partly  right  and  partly 
wrong. 

Under  certain  conditions  it  is  not  bad  practice  to  use  continuous 
trusses,  and  under  others  it  is,  irrespective  of  the  question  of  economics. 
When  the  foundations  of  the  piers  are  solid  rock  or  other  very  hard  material, 
continuity  is  permissible;  but  when  they  are  piles  or  comparatively  soft 
material  without  piles,  it  is  better  to  forego  any  possible  saving  of  metal 
rather  than  to  run  the  risk  of  unequal  settlement  of  piers  and  the  conse- 
quent upsetting  of  stress  distribution  throughout  the  trusses  from  end 
to  end  of  structure. 

The  most  notable  example  of  continuous  trusses  in  America,  or,  as  far 
as  the  author  knows,  anywhere  else  in  the  world,  is  the  Sciotoville  Bridge 
over  the  Ohio  River  on  the  Hne  of  the  Chesapeake  and  Ohio  Northern  Rail- 
road. At  this  location  continuous  trusses  were  permissible,  for  the  reason 
that  the  pier  foundations  are  sohd  rock  at  no  great  distance  below  the  bed 
of  the  stream.  That  structure  consists  of  two  continuous,  double-track- 
railway  spans  of  775  feet  each.  It  was  designed  and  engineered  by  Dr. 
Gustav  Lindenthal,  Consulting  Engineer,  and  was  completed  in  1917. 

Desiring  to  have  this  comparison  of  weights  of  metal  for  continuous 
trusses  conform  as  closely  as  possible  with  actual  conditions,  the  author 
assumed  the  outhnes  of  the  Sciotoville  structure,  and  contrasted  it  with  a 
bridge  of  two  simple  spans,  each  made  five  (5)  feet  shorter,  so  as  to  allow  for 
the  dist9,nce  between  centers  of  pedestals  on  the  middle  pier,  using  prac- 
tically the  same  panel-lengths  as  those  of  the  Sciotoville  Bridge  and  eco- 
nomic truss-depths  for  the  simple  spans  based  upon  the  information  given 
in  "Bridge  Engineering." 

75 


76  ECONOMICS   OF   BRIDGEWORK 

These  two  layouts  are  shown  in  Figs.  11a  and  116. 


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Chapter  XI 


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The  first  series  of  computations  was  made  upon  the  basis  of  adopting 
the  Petit-truss  type;  and  there  was  assumed  a  unit  load  of  1,000,000  lbs. 
applied  at  one  panel  point  at  a  time,  the  stresses  therefrom  Ixnng  found 
for  each  main  member  of  each  span  affected  by  the  loading.     These 


ECONOMICS  OP  CONTINUOUS  AND  NON-CONTINUOUS  TRUSSES         77 

stresses  were  summed  up  for  greatest  tension  and  greatest  compression  on 
each  piece,  in  order  to  determine  by  slide  rule  the  live  load  stresses.  The 
live  load  assumed  for  each  track  was  the  author's  Class  60  loading. 

In  order  to  save  time  and  labor,  a  constant  percentage  for  impact  was 
included  in  the  live  load  itseK  instead  of  varying  the  percentage  amounts 
to  be  added  to  the  live-load  stresses  in  the  different  web  members.  This 
approximation,  of  course,  caused  certain  errors  in  web  stresses;  but  their 
effects  on  the  two  contrasted  types  of  structure  were  practically  ahke,  and, 
therefore,  did  not  affect  the  correctness  of  the  comparison.  The  reactions 
for  concentrated  loads  in  the  coritinuous-truss  structure  were  obtained 
by  the  Theorem  of  Three  Moments.  No  attempt  was  made  to  correct 
later  the  stresses  thus  found  by  the  more  exact  method  of  least  work; 
for  the  reactions  obtained  in  that  manner  by  the  designers  of  the  Sciotoville 
Bridge  indicated  that  the  difference  in  total  weight  of  metal  caused  thereby 
was  trifling. 

The  finding  of  the  live-load  stresses  was  a  comparatively  simple  matter, 
but  the  determining  of  the  dead-load  stresses  was  much  more  arduous, 
because  sometimes  the  correct  distribution  of  the  metal  between  the  vari- 
ous panel-points  was  not  ascertained  until  the  third  trial.  No  attention 
was  paid  to  wind  stresses;  because,  in  double-track  railway-bridges  of  long 
span  and  heavy  live-loading,  the  excess  intensities  of  working  stresses 
allowed  in  modern  bridge  specifications  for  combinations  of  wind  stresses 
and  other  stresses  result  in  rendering  wind  stresses  in  the  trusses  entirely 
negligible. 

After  the  hve-load  stresses  and  the  dead-load  stresses  for  both  the 
continuous  and  the  non-continuous  spans  had  been  computed,  they  were 
combined,  and  the  maximum  stress  on  each  piece  for  both  tension  and 
compression  was  recorded.  Then  the  sectional  areas  were  determined  by 
the  specifications  of  Chapter  LXXVIII  of  "Bridge  Engineering,"  ignoring, 
however,  all  effects  of  reversion;  after  which  the  total  weights  of  metal  in 
main  members  were  figured  for  both  layouts,  and  to  them  were  added  the 
proper  percentages  to  cover  weights  of  details,  thus  giving  the  comparing 
weights  of  metal  for  the  two  types  of  structure  under  consideration.  Much 
to  the  author's  surprise,  the  weights  thus  found  were  so  nearly  alike  that 
their  difference  amounted  to  a  small  portion  of  one  per  cent — so  small,  in 
fact,  as  to  be  negligible. 

It  had  been  intended  to  make  an  entirely  new  set  of  sectional  areas  and 
compute  the  resulting  weights  of  metal  for  both  types  on  the  basis  of 
caring  for  reversing  stresses  in  accordance  with  the  method  provided  in  the 
before-mentioned  specifications;  but  this  was  found  to  be  unnecessary, 
because  members  in  which  reversion  occurred  were  very  few,  and  both  the 
direct  and  the  indirect  effects  thereof  were  readily  determined.  By  "in- 
direct" effect  is  meant  in  this  case  the  increase  in  weight  of  metal  due  to 
augmentation  of  dead  load  caused  by  provision  for  reversal.  Here  again 
was  a  surprise,  for  the  effects  on  the  two  types  were  exactly  alike.    These 


78  ECONOMICS   OF  BRIDGEWORK  Chapter  XI 

computations  showed  that,  for  long-span,  double-track,  steam-railway 
bridges  of  the  Petit-truss  type,  there  is  no  economy  of  metal  whatsoever  in 
making  adjacent  spans  continuous  over  the  piers,  and  that  the  matter  of 
caring  for  or  ignoring  the  effects  of  reversing  stresses  does  not  in  any  way 
influence  the  economics. 

These  results  were  so  decided  and  the  coincidence  of  weights  was  so 
exact  that  at  first  the  author  thought  the  entire  question  was  settled;  but 
it  was  suggested  by  Mr.  Shortridge  Hardesty,  his  principal  designing 
engineer,  that,  if  the  divided-triangular  truss  adopted  for  the  Sciotoville 
Bridge  were  investigated,  a  different  result  might  be  found;  and  it  was 
decided  to  make  the  test.  The  layouts  of  trusses  for  the  new  comparison 
are  shown  in  Figs,  lie  and  lid.  The  computations  were  all  prepared  ex- 
actly as  before,  and  it  was  found  necessary  to  make  two  sets  of  figures  for 
the  continuous-truss  layout  before  the  correct  dead  load  was  determined. 
The  findings  of  this  second  set  of  computations  were  as  follows : 

In  the  simple-truss  spans  the  weights  of  metal  for  the  divided-triangular 
and  the  Petit  types  were  nearly  alike,  the  slight  difference  which  there  was 
being  in  favor  of  the  former;  and  the  continuous-truss  type  showed  a  gain 
of  twelve  per  cent  over  the  non-continuous  type  when  reversion  was 
ignored  and  eleven  per  cent  when  it  was  properly  provided  for. 

The  computations  made  up  to  this  stage  of  the  investigation  settled  the 
economics  for  long-span,  steam-railway  bridges;  but  it  was  seen  by  a 
'priori  reasoning  that  the  results  would  probably  be  somewhat  different  for 
standard  highway  bridges,  consequently  it  was  decided  to  repeat  the  cal- 
culations for  the  latter  structures.  To  this  end  the  total  loadings  (i.e., 
live  load  plus  dead  load)  were  retained,  but  a  different  division  thereof  was 
made  by  diminishing  the  live  loads  and  increasing  the  dead  loads,  so  as  to 
correspond,  as  nearly  as  may  be,  with  the  ratios  of  those  loads  in  modern 
highway  bridges  having  a  paved  roadway,  reinforced-concrete  base-slab, 
and  reinforced-granitoid  sidewalks  for  the  span-length  under  con- 
sideration. 

The  result  of  this  third  set  of  computations  showed  that  for  the  divided- 
triangular-truss  layout  there  was  an  economy  of  twenty-two  per  cent  in 
favor  of  the  continuous  trusses,  and  that  reversing  stresses  affected  very 
few  members  and  those  so  slightly  that  the  influence  of  reversion  could  be 
completely  ignored.  It  was  not  thought  worth  while  to  repeat  these  high- 
way-bridge calculations  for  the  Petit-truss  layouts. 

The  computations  made  thus  far  settled  the  comparative  economics  of 
continuous  and  non-continuous  trusses  for  long-span  bridges,  both  railway 
and  highway,  also  those  of  the  Petit  and  the  divided-triangular  trusses  for 
such  structures;  but  it  could  not  properly  be  assumed  that  what  was  found 
to  be  true  for  long  spans  would  apply  also  to  short  ones,  consequently  it 
was  decided  to  make  a  new  set  of  computations  for  comparatively-short- 
span  layouts  for  steam-railway  bridges  of  both  the  divided-triangular  truss 
and  the  Pratt-truss  types. 


ECONOMICS  OF  CONTINUOUS  AND  NON-CONTINUOUS  TRUSSES         79 


By  reducing  all  the  truss  dimensions  to  one  half,  it  was  practicable  to 
employ  without  change  the  previously-determined  index  stresses  (those 


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found  from  assumed  unit  loadings),  and  thus  the  labor  of  figuring  was 
greatly  reduced.  As  before,  the  dead-load  stress-computations  were 
repeated  until  the  assumed  and  the  resulting  dead  loads  at  the  different 


80 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XI 


panel  points  were  in  close  agreement.  The  results  of  this  fourth  set  of  cal- 
culations were  as  follows : 

The  divided-triangular-truss  figures  indicated  a  gain  of  seven  per  cent 
for  the  continuous-truss  layout  over  the  non-continuous  one  when  reversing 
stresses  were  ignored  and  no  gain  at  all  hut  simply  a  stand-off  when  they  were 
properly  provided  for.  But,  when  the  Pratt-truss  was  employed,  the  non- 
continuous-truss  layout  showed  a  gain  of  two  per  cent  over  the  continuous- 
truss  one  when  reversing  stresses  were  ignored  and  five  per  cent  when  they 
were  properly  provided  for. 

The  said  results  also  indicated  for  short,  simple-truss  spans  that,  when 
reversals  are  ignored,  there  is  no  difference  in  weight  of  metal  between 
steam-railroad  bridges  of  the  Pratt-truss  and  the  divided-triangular-truss 
types;  but  that,  when  reversals  are  properly  provided  for,  the  latter  has 
an  advantage  of  five  per  cent. 

It  was  not  deemed  worth  while  to. compute  the  economics  for  highway 
bridges  of  short  spans;  but  it  might  be  inferred  by  a  'priori  reasoning,  based 
on  the  preceding  results,  that,  in  the  case  of  the  divided-triangular  trussing, 
the  continuous  spans  would  have  an  advantage  of  thirteen  per  cent  when 
reversals  are  ignored  and  twelve  per  cent  when  they  are  properly  cared  for — 
also  that  in  the  case  of  the  Pratt  trussing  there  would  be  no  material  ad- 
vantage in  continuity. 

Without  making  another  set  of  computations,  the  author  would  not 
care  to  employ  a  priori  reasoning  for  the  determination  of  the  comparative 
economics  of  continuous  and  non-continuous  trusses  in  long-span,  highway 
bridges  of  the  Petit-truss  type,  excepting  that  it  seems  pretty  safe  to  assume 
that  the  Petit  trussing  would  have  no  advantage  over  the  divided-triangu- 
lar trussing,  and  that  the  continuous  trusses  would  probably  show  a  small 
advantage  over  the  non-continuous  ones. 

All  the  actual  results  of  the  calculations  made  for  this  study  are  col- 
lected in  the  two  following  tables,  and  are  expressed  in  ratios,  unity  stand- 
ing for  weights  of  continuous  divided-triangular  trusses  when  the  effect  of 
reversals  is  ignored. 

TABLE   11a 
SUMMARY   OF   WEIGHT  RATIOS 
Divided-Triangular  Trussing 


Span  Length 

Type  of 
Bridge 

Reversals  Ignored 

Reversals  Considered 

in  Feet 

Continuous 

Simple 

Continuous 

Simple 

77.5 
77.5 
387^ 

Railway 
Highway 
Railway 

i.no 

1.00 
1.00 

1.12 
1.22 
1.07 

1,03 
1.00 
1.10 

1.14 
1.22 
1.10 

ECONOMICS  OF  CONTINUOUS  AND  NON-CONTINUOUS  TRUSSES        81 


TABLE    116 
Petit  or  Pratt  Trussing 


Span  Length 

Type  of 
Bridge 

Reversals  Ignored 

Reversals  Considered 

in  Feet 

Continuous 

Simple 

Continuous 

Simple 

775 
3871 

Railway 
Railway 

1.13 
1.09 

1.13 
1.07 

1.16 
1.20 

1.16 
1.15 

In  determining  the  comparative  economics  of  continuous  and  non-con- 
tinuous trusses  for  any  proposed  bridge,  the  application  of  the  preceding 
findings  would  have  to  be  somewhat  modified  in  case  the  structure  has  to  be 
erected  by  semi-cantilevering.  Under  such  a  condition  the  continuous 
trusses  have  an  advantage  over  the  non-continuous  ones,  at  least  to  the 
extent  of  the  extra  metal  required  by  the  toggles  for  the  latter  over  the 
center  pier.  Again,  it  is  probable  that  some  of  the  lighter  truss  members  in 
either  type  will  need  reinforcing  for  erection  stresses;  and  this  consideration 
is  likely  to  affect  the  non-continuous  trusses  more  adversely  than  it  does 
the  continuous  ones. 

Summary  of  Conclusions 

Summarizing  the  results  of  the  entire  investigation,  the  following  con- 
clusions are  reached: 

First.  For  long  spans  the  divided-triangular  trussing  is  decidedly 
superior  to  the  Petit  trussing  for  bridges  with  continuous-truss  spans,  but 
not  much  so,  if  at  all,  for  those  of  simple-truss  spans. 

Second.  For  long  spans  there  is  an  important  saving  of  metal  by  the 
adoption  of  continuous  trusses,  and  the  said  saving  is  nearly  twice  as  great 
for  standard  highway  bridges  as  for  modern,  double-track  railway-bridges. 

Third.  For  long-span  bridges  the  method  of  treating  the  matter  of 
stress  reversal  has  practically  no  effect  upon  the  comparative  economics  of 
continuous  and  non-continuous  trusses. 

Fourth.  For  comparatively-short-span,  steam-railway  bridges,  the 
continuous  truss  has  a  small  advantage  over  the  simple  truss  only  when  the 
divided-triangular  trussing  is  used  and  stress  reversals  are  ignored.  In 
all  other  cases  the  comparison  is  either  a  stand-off  or  in  favor  of  the  simple 
truss. 

Fifth.  For  comparatively-short-span,  steam-railway  bridges,  the 
divided-triangular  trussing  is  generally  more  economic  of  metal  than  the 
Pratt  trussing. 

Sixth.  In  no  case  should  either  the  Pratt  or  the  Petit  truss  be  employed 
for  continuous  spans,  because  in  these  the  divided-triangular  truss  is  more 
economic. 


82  ECONOMICS   OF   BEIDGEWORK  Chapter  XI 

Seventh.  In  case  of  a  structure  requii'ing  erection  by  semi-cantilevering 
the  continuous  truss  will  possess  an  advantage  over  the  non-continuous 
one,  at  least  to  the  extent  of  the  weight  of  extra  metal  required  by  the  toggle 
for  connecting  temporarily  over  the  center  pier  the  inner  hips  of  the  two 
simple-truss  spans.  This  advantage  may  even  extend  to  the  reinforce- 
ment for  erection  stresses,  but  if  it  does,  the  gain  thus  involved  can  never 
be  very  great. 


CHAPTER  XII 

COMPAKATIVE  ECONOMICS  OF  SIMPLE-TRUSS  AND  CANTILEVER  BRIDGES 

About  the  time  that  cantilevers  came  into  vogue,  some  twenty-five  or 
thirty  years  ago,  certain  bridge  designers  entertained  a  wild  idea  to  the 
effect  that  the  new  type  involved  some  special  virtue  or  feature  of  excellence 
or  else  that  it  was  economic  in  first  cost;  because  many  cantilever  bridges 
were  built  in  places  where  simple-span  structures  would  have-  been  far 
better  and  cheaper.  Possibly  the  thought  of  estabhshing  an  innovation 
induced  some  of  the  designers  of  those  bridges  to  prefer  the  cantilever  type 
to  that  of  the  simple  truss.  What  a  pity  it  is  that  such  designers  did  not 
devote  their  time  and  energy  to  an  attempt  to  introduce  the  steel-arch 
bridge  into  American  practice!  Had  they  done  so,  probably  they  would 
have  been  successful;  because  there  is  often  true  economy  in  the  arch — 
besides  it  is  far  more  aesthetic  than  either  the  cantilever  or  the  simple  truss. 
A  long-span,  cantilever  bridge  can  be  made  agreeable  to  the  eye  by  using 
artistic  outlines  and  a  well-studied  web-system;  and,  again,  its  simple 
vastness  produces  a  pleasing  impression  upon  the  beholder;  but  a  small- 
span  cantilever  is  ugly  and  causes  a  trained  intelligence  to  propound  to 
itself  the  question  "why  and  wherefore?"  without  receiving  a  satisfying 
answer. 

It  is  true  that  for  certain  fairly-narrow  crossings  the  water  is  so  deep,  or 
the  current  is  so  swift,  that  the  use  of  falsework  is  out  of  the  question,  and 
that  the  adoption  of  cantilevering  during  erection  is  necessitated.  Such 
conditions,  however,  do  not  require  cantilever  bridges,  but  semi-cantilevers, 
i.e.,  structures  that  are  cantilevers  during  erection  and  either  simple  spans 
or  arches  afterwards.  This  method  of  erection  for  simple-truss  spans  was 
first  evolved  by  the  author  some  twenty-five  or  thirty  years  ago,  but  was 
not  actually  used  by  him  in  construction  until  some  time  later.  A  descrip- 
tion of  it  will  be  found  in  Chapter  XXV  of  "Bridge  Engineering." 

It  is  evident  to  any  engineer  who  gives  the  subject  due  consideration 
that  a  cantilever  bridge  is  less  rigid  than  the  corresponding  simple-truss 
structure,  because  its  vertical  deflections  under  live  load  are  necessarily 
larger,  thus  permitting  more  vibration  as  well  as  greater  irregularity  in  the 
track  grade;  hence,  for  steam-railway  bridges,  other  things  being  equal,  the 
simple-truss  layout  should  be  chosen — or  even  if  it  should  cost  somewhat 
more,  because  rigidity  is  an  important  consideration  in  the  operation  of 
steam-railway  trains.  For  highway  and  electric-railway  bridges,  though, 
it  is  not  of  such  great  importance;  consequently,  if  in  these  structures  the 

83 


84  ECONOMICS   OF   BRIDGEWORK  Chapter  XII 

cantilever  should  show  even  a  small  economy  in  the  comparison,  it  would 
be  well  to  adopt  it. 

The  question  of  what  is  the  economic  limit  of  length  of  simple-truss 
spans  as  compared  with  cantilevers  is  still  a  mooted  one.  Professors  Merri- 
man  and  Jacoby,  on  page  119  of  Part  IV  of  their  excellent  treatise  on  "Roofs 
and  Bridges,"  state  that  the  economic  limit  for  smiple  spans  was  probably 
nearly  reached  in  the  building  of  the  five  hundred  and  eighty-six  (586)  foot 
span  over  the  Great  Miami  River  at  Elizabethtown  near  Cincinnati;  but 
the  author  has  had  occasion  to  compare  simple-truss  spans  of  somewhat 
greater  length  than  that  with  the  corresponding  cantilever  structures  and 
has  found  them  more  economic.  The  continuity  of  cantilever  spans  in 
resisting  wind  loads  lowers  the  requirement  for  minimum  width  from  one- 
twentieth  (1/20)  to  one-twenty-fifth  (1/25)  of  the  greatest  span-length, 
and  hence,  because  of  substructure  considerations,  gives  an  advantage  to 
the  cantilever  type  that  in  certain  extreme  cases  will  more  than  offset  its 
disadvantage  of  greater  weight  of  truss  metal. 

This  question  of  when  to  pass  from  simple-truss  spans  to  cantilevers 
is  not  affected  very  much  today  by  the  last  consideration,  because  bridges 
with  spans  long  enough  to  necessitate  the  comparison  are  often  so  wide 
as  to  cause  it  to  be  ignored.  For  instance,  one  seldom  hears  any  more 
of  a  single-track  railway  bridge  having  a  span  longer  than  four  hundred 
(400)  feet;  and  first-class,  double-track,  steam-railway  bridges  have  a 
clearance  of  twenty-eight  (28)  or,  preferably,  thirty  (30)  feet,  thus 
making  the  distance  between  central  planes  of  trusses  from  thu'ty-two  (32) 
to  thirty-four  (34)  feet.  The  limiting  simple-truss  span-length  established 
by  good  American  practice  for  the  latter  dimension  is  six  hundred  and 
eighty  (680)  feet,  and  for  cantilevers  it  is  eight  hundred  and  fifty  (850)  feet. 

Of  still  greater  importance  are  the  special  requirements  that  govern 
the  layout  at  each  site.  Fig.  12a  (which  is  a  reproduction  of  Fig.  55aaa 
on  page  1271  of  ''Bridge  Engineering"),  shows  typical  layouts  for  cantilever 
bridges.  There  is  still  another  type,  consisting  of  equal  (or  nearly  equal) 
spans  with  short  cantilever  arms,  that  is  discussed  later  in  this 
chapter. 

The  Type-C-eantilever  bridge,  which  has  three  spans  of  practically 
ec}ual  lengths,  will  first  be  considered.  It  will  be  compared  with  a  cor- 
responding structure  having  three  simple-truss  spans.  These  layouts 
apply  where  the  distance  between  end  piers  is  fixed,  while  the  intermediate 
piers  can  be  placed  where  desired.  Fig.  126  gives  the  comparing  weights 
for  pin-connected,  double-track-railway  bridges.  From  its  curves  one  can 
see  that  the  span  of  equal  cost  is  about  six  hundred  and  thirty  (630)  feet. 
It  may  be  possible  to  reduce  the  cantilever  weights  by  varying  the  sizes 
of  the  openings  and  the  relative  length  of  suspended  span  to  cantilever 
arm ;  but,  even  with  such  changes,  it  is  not  likely  that  the  span-length  for 
equal  weights  of  metal  would  be  as  low  as  six  hundred  (600)  feet. 

In  the  case  of  highway  bridges,  the  weights  of  metal  per  lineal  foot  in 


ECONOMICS   OF   SIMPLE-TRUSS   AND   CANTILEVER   BRIDGES 


85 


cantilevers  would  be  about  the  same  as  those  for  simple-truss  spans  of  five 
hundred  and  fifty  (550)  or  five  hundred  and  seventy-five  (575)  feet. 


■^ 


-^ 


"^ 


g 


•-^ 


-^ 


"^ 


h-r 


^ 


^ 


•^ 


>^^ 


-^ 


m 


o 


§1 


03 


It  is  unnecessary  to  consider  the  comparative  economics  of  simple- 
spans  and  cantilevers  for  electric-railway  bridges  pure  and  simple.    Nobody 


86 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XII 


is  ever  going  to  build  any  of  them  of  long-enough  span  to  bring  up  the 
question,  because  such  expensive  structures  would  surely  be  constructed  to 
accommodate  highway  traffic  also. 

The  type  of  cantilever  under  discussion  (Type  C  of  Fig.  12a)  is  not  well 
adapted  to  crossings  where  falsework  cannot  be  emploj^ed;  and  the  use  of 
the  simple-span  layout,  in  which  the  central  span  can  be  cantilevered  out 
from  the  side  ones,  is  frequently  preferable  on  this  account.  Also  the 
adoption  of  the  three  duplicate  spans  or  even  the  duphcate  side  spans  will 

.0        100       200      300       400       500       600      700       600       900     1000 


40.000 


35000 


30000 


25000 


20.000 


15000 


\  10 000 


5000 


900 


1000 


0  m        200        200        400         500        600        700        SOi 

Length  of  5/mp/e  Span  in  reef 

Fig.  126.     Comparative  Weights  of  Metal  for  Double-Track,  Simple-Truss  Bridges 

and  Type-C-Cantilever  Bridges. 

usually  cause  a  small  reduction  in  the  pound  price  of  the  manufactured 
metal,  as  compared  with  that  for  the  cantilever. 

The  cantilever  layout  denominated  Type  A  in  Fig.  12a  is  the  most 
common  of  the  four  types  illustrated.  It  is  generally  used  for  a  long- 
span  structure  where  the  length  of  the  central  openings  is  fixed,  while  the 
lengths  of  the  end  spans  can  be  made  much  shorter.  Also,  it  is  more 
likely  to  be  adopted  where  the  central  span  cannot  be  erected  on  falsework. 
For  these  reasons  it  cannot  fairly  be  contrasted  with  a  siniplc-truss,  equal- 
span  layout,  nor  with  the  Type-C  cantilever.  It  may  very  properly, 
though,  be  pitted  against  a  simple-truss  layout  with  imequal  sixms— in 
fact  the  same  spans  as  the  cantilever  layout  has.  Fig.  12c  gives  curves  of 
weights  for  such  layouts,  for  pin-connected,  double-track,  steam-railway 


ECONOMICS   OF   SIMPLE-TRUSS   AND    CANTILEVER   BRIDGES        87 


bridges.  It  will  be  noted  that  the  span-length  for  equal  weights  is  about 
620  feet.  If  the  central  span  must  be  erected  by  cantilevering,  extra  metal 
will  be  required  for  the  simple-truss  layout,  amounting  to  about  8  per 
cent  of  the  truss-weight.  The  span-length  for  equal  weights  will  then  be  a 
little  over  500  feet. 

If  the  side-spans  in  the  simple-truss  layout  be  replaced  by  steel  trestle, 
the  span  length  for  equality  of  weights  will  be  about  700  feet  when  the 
central  span  is  erected  on  falsework.  This  layout,  evidently,  cannot  be 
used  when  the  central  span  must  be  cantilevered  out. 

The  Type-A  cantilever  of  the  proportions  shown  in  Fig.  12a  is  usually 
an  uneconomic  layout  to  adopt  when  the  distance  between  the  end  piers  is  a 
0        100       ZOO       300       400       500       600       700      300       900     1000 


mooo 


30.000 


25.000 


20.000 


15.000 


10.000 


5.000 


Fig.  12c. 


100       200        300        400        500        600 

Lentjth  of  Cenfral  Span  in  Feet 

Comparative  Weights  of  Metal  for  Double-Track,   Simple-Truss  Bridges 
and  Type-A-Cantilever  Bridges. 


fixed  quantity,  while  the  two  intermediate  piers  can  be  placed  where 
desired.  For  such  a  location  there  should  generally  be  used  three  simple- 
truss  spans,  a  Type-C  cantilever,  or  a  cantilever  with  the  end  spans  nearly 
as  long  as  the  central  span.  As  before  stated,  this  latter  layout  is  discussed 
subsequently  in  this  chapter.  In  many  cases,  however,  the  piers  of  the 
Type-A  cantilever  with  a  long  central  span  will  be  much  cheaper  than  those 
of  the  simple-span  bridge,  on  account  of  their  being  nearer  to  the  banks 
of  the  river.  For  such  a  crossing,  the  total  cost  of  the  simple-span  struc- 
ture can  sometimes  be  reduced  by  lengthening  the  center  span  and  shorten- 
ing the  side-spans;  and  the  most  economic  layout  for  the  simple-span  bridge 
should  first  be  found,  and  its  total  cost  then  compared  with  that  of  the 
cantilever  structure. 

There  is  an  economic  consideration  of  some  importance  in  the  compari- 
son of  simple-truss  and  cantilever  bridges  which,  as  far  as  the  author  knows, 


88  ECONOMICS    OF   BEIDGEWORK  Chapter  XII 

has  never  yet  been  given  any  attention — at  least  none  in  print.  It  indi- 
cates within  rather  narrow  hmits  a  sHght  economy  for  the  cantilever  type, 
but  the  amount  thereof  and  the  location  of  the  said  limits  are  dependent 
upon  several  considerations,  among  which  the  most  important  are  the  fol- 
lowing: 

A.  Average  length  of  spans  considered. 

B.  Ratio  of  live  load  plus  impact  to  total  load. 

C.  Method    adopted    for    combining    reversing    stresses,    when 

proportioning  sections  of  members. 

The  best  conception  of  this  matter  of  economics  can  be  obtained  from  a 
dissertation  based  upon  an  assumed  layout  of  simple-truss  spans,  all  of 
equal  length, — for  instance,  a  long  succession  of  like  spans  of  two  hundred 
feet  each,  the  panel-lengths  being  twenty  feet.  If  now  we  extend  the 
trusses  of  every  other  span  one  panel  beyond  each  of  its  piers  and  sus- 
pend from  the  cantilevered  ends  thus  formed  the  shortened  intermediate 
spans,  we  shall  have  a  cantilever  bridge  that  will  effect  a  saving  in  weight 
of  metal  in  every  span.  It  is  evident  without  any  figuring  at  all  that  the 
spans  which  contain  the  suspended  trusses  will  weigh  less  than  the  simple- 
truss  spans,  because  the  suspended  portion  is  decidedly  lighter  and  the 
cantilever  arms,  being  so  short,  cannot  be  very  heav3^  Again,  the  dead 
load  stresses  in  the  chords  of  the  other  spans  are  somewhat  reduced,  but 
probably  not  enough  to  permit  of  any  reversion  of  stress  when  the  span  is 
empty  with  the  adjoining  spans  loaded.  The  total  stresses  in  chords  are, 
therefore,  materially  smaller  than  those  for  the  simple-truss  spans,  resulting 
in  an  economy  of  metal,  notwithstanding  the  fact  that  there  are  two 
extra  panel-lengths  of  top  chord  involved  by  the  change  from  simple-span 
type  to  cantilever  type,  and  that  the  vertical  posts  over  the  piers  combined 
with  the  end  main  diagonals  are  somewhat  heavier  than  the  inclined  end 
posts  of  the  simple-truss  span.  On  the  other  hand,  though,  the  canti- 
lever structure,  having  only  one  pair  of  pedestals  per  pier,  involves  a  slight 
economy  of  "metal  on  piers"  and  permits  the  width  of  pier-top  to  be 
reduced  a  little  below  that  required  for  the  two  pedestals  of  consecutive 
trusses  in  the  simple-truss  layout,  which  saving  in  some  cases  will  extend 
from  coping  to  bottom  of  caisson. 

Next,  let  us  assume  that  there  are  cantilever  extensions  of  two  panel 
lengths  instead  of  one.  There  may  or  may  not  be  a  material  saving  of 
metal  in  those  spans  containing  the  suspended  trusses  in  comparison  with 
simple-truss  spans,  although  there  will  be  some  reduction ;  for,  while  there 
is  a  decided  lessening  in  the  weight  of  metal  per  lineal  foot  in  the  sus- 
pended portion,  the  cantilever  arms  tend  to  become  heav}^  In  the  chords 
of  the  other  spans,  the  dead-load  stresses  are  made  very  small,  permitting 
some  reversion  therein  from  the  live  loads  on  the  adjoining  spans;  and  the 
result  will  probably  involve  an  increase  in  woiglit  of  truss  metal.  The  net 
effect  of  the  change  in  layout  upon  the  struciuie  as  a  whole  is  uncertain; 
but  it  is  probably  slightly  uneconomic  of  metal. 


ECONOMICS    OF    SIMPLE-TRUSS   AND    CANTILEVER   BRIDGES         89 

If  the  assumption  be  made  that  three  panel-lengths  be  cantilevered,  it 
is  almost  certain  that  the  total  weight  of  metal  in  the  structure  will  be 
augmented. 

It  is  evident  that  the  proportionate  effect  of  the  cantilevering  under 
consideration  is  dependent  upon  whether  the  bridge  is  a  railroad  structure  or 
a  highway  one  with  a  paved  roadway  supported  on  a  reinforced-concrete 
base,  because  the  relative  effect  of  reversion  is  far  greater  in  the  former  case 
than  in  the  latter;  hence  an  amount  of  cantilevering  of  this  kind  that  would 
be  uneconomic  in  a  railroad  bridge  might  be  truly  economic  in  the  cor- 
responding highway  structure. 

As  the  span-length  increases,  the  ratio  of  live  load  to  total  load  decreases, 
and  hence  the  proportionate  effect  on  weight  of  metal  due  to  reversing 
stresses  diminishes.  For  this  reason  one  can  anticipate  that  the  longer  the 
average  span  the  greater  will  be  the  relative  importance  of  the  economic 
feature  of  design  under  consideration. 

Finally,  the  saving  in  metal  (or  the  reverse)  by  this  method  of  cantilever- 
ing is  fundamentally  dependent  upon  the  manner  in  which  the  designing 
specifications  take  care  of  reversing  stresses.  If  these  be  entirely  ignored, 
as  some  engineers  advocate  doing,  the  cantilevering  will  effect  a  large 
economy  of  metal,  even  when  the  cantilever  arms  are  comparatively  long; 
whereas,  if  these  stresses  of  opposite  sign  are  cared  for  by  adding  to  the 
larger  three-quarters  of  the  smaller  and  proportioning  for  the  sum,  the 
saving  will  be  but  little,  if  any.  The  most  approved  and  up-to-date  prac- 
tice is  to  add  to  the  larger  stress  only  one-half  of  the  smaller;  and  in  that 
event  some  economy  may  be  anticipated,  provided  that  the  length  of  the 
cantilever  arms  be  not  too  great. 

If,  with  a  layout  such  as  is  being  considered,  there  be  found  for  openings 
of  equal  size  an  economy  in  a  certain  amount  of  cantilevering,  the  question 
arises  "would  there  not  be  a  further  saving  of  metal,  if  the  lengths  of  the 
continuous  spans  were  to  remain  fixed  and  those  of  the  other  spans  were  to 
be  moderately  increased?  "  The  answer  to  this  question,  in  all  probability, 
is  affirmative,  although  the  economy  involved  would  not  be  important. 

In  view  of  the  preceding  dissertation,  it  is  evident  that  it  is  entirely 
impracticable  to  give  any  quantitative  solution  to  this  economic  question, 
but  that  it  must  be  solved  for  each  case  as  it  arises.  In  railroad  bridge 
designing  the  matter  is  not  important;  because  it  is  highly  improbable  that 
the  value  of  the  metal  saved  would  offset  the  disadvantage  of  the  reduction 
in  rigidity  that  is  unavoidable  when  changing  from  the  fixed-span  type  to 
that  of  the  cantilever.  But  in  the  case  of  a  highway  bridge  with  a  heavj' 
floor,  it  is  an  altogether  different  matter,  because,  as  previously  pointed  out, 
rigidity  is  not  so  fundamentally  important  in  highway  structures  as  it  is  in 
railway  bridges;  and,  moreover,  the  stiff  concrete  slab  itself  increases  so 
greatly  the  rigidity  of  the  steel  construction  that  the  detrimental  looseness 
caused  by  the  hinged  attachments  of  the  suspended  span  loses  most  of  its 
importance. 


CHAPTER  XIII 

COMPARATIVE    ECONOMICS    OF    CANTILEVER    AND    SUSPENSION    BRIDGES 

This  chapter  is  essentially  a  reproduction  of  a  paper  delivered  by  the 
author  to  the  Western  Society  of  Engineers  at  Chicago  on  September  15th, 
1919.     It  is  reproduced  here  practically  in  full  for  two  reasons: 

First.  Outside  of  the  membership  of  that  society,  the  paper  has  been 
read  very  httle,  and  it  did  not  receive  any  written  discussion;  consequently, 
its  contents,  as  far  as  this  treatise  and  the  engineering  profession  in  general 
are  concerned,  are  practically  new  material. 

Second.  Unless  it  be  shown  herein  that  most  of  the  information  which 
had  been  published  about  the  subject  prior  to  September,  1919,  was 
wrong,  there  would  not  be  much  use  in  the  author's  stating  that  such  is  the 
fact  and  claiming  correctness  for  the  data  thereon  which  he  presents; 
because  in  engineering,  as  in  all  other  walks  of  life,  any  man's  word  is  as 
good  as  another's  on  a  disputed  point  until  one  has  given  absolute  proof  of 
the  correctness  of  his  claim.  Moreover,  from  the  strictly-professional 
point  of  view,  the  demonstration  of  the  author's  findings  and  the  record  of 
the  various  steps  which  he  took  in  his  investigation  ought  to  prove  fairly 
interesting  reading— at  least  to  structural  engineers  and  students  of  the 
specialty  of  bridge  design  and  construction.  But  if  any  reader  should  feel 
averse  to  wading  through  this  long  chapter,  he  can  easily  arrive  at  the 
results  of  the  somewhat-elaborate  study  by  skipping  to  near  the  end  of  it, 
where  he  will  find  a  resume  of  conclusions. 

The  calculations  for  the  suspension  bridges  were  prepared  upon  the 
basis  that  the  stiffening  trusses  were  free  at  their  ends;  but  later  some  more 
computations  were  made  in  order  to  determine  the  effect  upon  the  economic 
deductions,  under  the  assumption  that  the  said  ends  were  anchored,  but 
not  fixed,  to  the  masonry.  The  results  showed  for  both  the  longer  and  the 
shorter  spans  a  decrease  of  nearly  one  hundred  feet  in  the  span-length  for 
equal  cost.  This  is  not  a  serious  difference,  nevertheless  it  is  well  to  remem- 
ber that  it  exists. 

The  following  is  a  reproduction  of  the  previously-mentioned  paper: 

The  Comparative  Economics  of  Cantilever  and  Suspension 

Bridges 

Under  the  title  "Suspension  Bridges  and  Cantilevers — Their  Economic 
Proportions  and  Limiting  Spans,"  Dr.  D.  B.  Steinman  in  1911  issued  a  little  ' 

90 


ECONOMICS  OF  CANTILEVER  AND  SUSPENSION  BiRIDGES  91 

book  in  the  Van  Nostrand  Science  Series;  and  in  1913  he  produced  a  second 
edition  of  it  with  a  few  revisions  and  the  addition  of  four  folding  plates. 

In  that  treatise  he  draws  the  conclusion  that  "the  critical  span  at 
which  the  suspension  bridge  becomes  economically  superior  to  the  canti- 
lever bridge  is  1,670  feet."  His  calculations  were  made  for  a  structure 
carrying  four  steam  railway  tracks  between  trusses  and  two  exterior  side- 
walks on  the  lower  deck,  and  a  roadway  with  electric  railway  tracks 
between  trusses  on  the  upper  deck,  the  total  live  load  for  the  trusses  being 
18,000  pounds  per  linear  foot,  of  which  12,000  pounds  were  for  the  steam 
railways.  His  profile  shows  bare  bed  rock,  which,  under  the  approaches, 
is  approximately  horizontal  and  a  few  feet  above  extreme  high-water  level. 
He  figured  his  cantilever  structures  for  main  openings  of  1,000  feet,  1,500 
feet,  and  2,000  feet,  and  his  suspension  bridges  for  main  openings  of  1,500 
feet,  2,250  feet,  and  3,000  feet. 

While  recognizing  the  value  of  Dr.  Steinman's  work  and  giving  him  due 
credit  for  his  laudable  energy  and  ambition,  the  author  doubted  the  cor- 
rectness of  the  main  conclusion  just  mentioned,  and  in  "Bridge  Engineer- 
ing" he  wrote  concerning  it  as  follows: 

"In  order  to  evolve  a  mathematical  demonstration  of  the  problem,  he  (Dr.  Stein- 
man)  had  to  make  numerous  assumptions  more  or  less  approximately  correct.  Without 
checking  all  of  his  mathematical  work,  it  is  evident  that  the  professor  has  made  as 
fair  a  comparison  as  he  could;  but  his  assumptions  were  so  numerous  and  approximate 
that  his  conclusions  must  be  taken  with  a  liberal  allowance  for  variation.  .   .  . 

"All  these  facts  affect  materially  the  question  at  issue,  and  it  is  probable  that,  if  the 
changes  implied  were  incorporated,  the  span  length  for  equal  cost  found  by  the  inves- 
tigator would  be  considerably  greater." 

For  a  number  of  years  the  author  has  had  the  desire  to  settle  this 
economic  question;  but  the  amount  of  labor  involved  had  always  appeared 
appalling.  In  truth,  it  was  so,  because  Dr.  Steinman  spent  most  of  his 
spare  time  for  two  years  in  making  the  computations  for  his  investigation. 

It  is  true  that  the  author  could  easily  have  figured  the  weights  of  metal 
and  the  costs  thereof  for  cantilever  bridges  by  employing  the  diagrams 
which  he  prepared  for  his  papers  on  "Nickel  Steel  for  Bridges,"*  and  "The 
PossibiKties  in  Bridge  Construction  by  the  Use  of  High- Alloy  Steels/'* 
most  of  which  diagrams  were  published  in  these  papers;  but  not  until 
after  he  had  written  Chapter  XXVII  of  "Bridge  Engineering"  did  he 
possess  any  quick  method  of  computing  the  weights  of  metal  and  the  costs 
of  suspension  bridges.  In  that  chapter  are  presented  for  the  first  time  a 
number  of  formulae,  from  which,  in  conjunction  with  the  numerous  dia- 
grams in  Chapter  LV  of  the  same  treatise,  can  be  found  quite  readily  the 
approximate  weights  of  metal  for  all  portions  of  suspension  bridges. 

In  April,  1918,  for  the  first  time  since  the  issuing  of  his  book,  the  author 
found  leisure  to  make  the  contemplated  economic  investigations.     They 

*  Published  in  the  Transactions  of  the  American  Society  of  Civil  Engineers. 


02  ECONOMICS   OF  BRIDGEWORK  Chapter  XIII 

occupied  all  of  his  spare  time  for  a  month  and  a  haK,  representing  alto- 
gether some  300  hours  of  steady  figuring.  As  in  the  case  of  his  paper  on 
"The  Possibihties  in  Bridge  Construction  by  the  Use  of  High-Alloj"  Steels," 
he  did  all  of  the  computation  work  entirely  unaided,  checking  the  results 
himself,  but  relying  for  their  correctness  mainly  upon  the  regularity  of  the 
platted  curves. 

As  his  data  on  weights  of  metal  in  cantilever  bridges  were  primarily 
for  double-track-railway  structures,  his  first  investigation  was  made  for 
that  class  of  bridges,  using  the  Uve  loads,  impact,  and  specifications  indi- 
cated in  the  two  previously-mentioned  papers.  For  convenience  of  com- 
parison, he  assumed  Dr.  Steinman's  unit  prices  for  metal  in  place,  but  for 
substructure  estimating  he  adopted  the  method  which  he  has  employed 
for  many  years,  viz.,  using  a  unit  price  for  concrete  above  low  water,  another 
for  the  mass  of  the  pneumatic  caissons  with  their  superimposed  cribs  below 
low  water,  auQther  for  the  corresponding  mass  below  the  same  in  box 
cribs  filled  with  concrete  resting  on  piles,  and  a  price  per  lineal  foot  for 
those  portions  of  the  said  piles  projecting  below  the  bases  of  the  cribs. 
These  unit  prices  are  as  follows: 

Shafts  and  walls S15 .  00  per  cu.  yd. 

Mass  of  pneumatic  caissons  with  their  cribs  25 .  00  per  cu.  yd. 
Mass  of  box  cribs,  including  enclosed  por- 
tions of  piles 20 .  00  per  cu.  yd. 

Piles  projecting  below  base  of  crib 1 .  50  per  lin.  ft. 

The  unit  prices  for  metal  in  place  were  as  follows : 

Wire  cables , 12 . 5)!f  per  lb. 

Nickel  steel 8.0^  per  lb. 

Carbon  steel  in  spans 5.6^  per  lb. 

Carbon  steel  in  trestle  approaches 5.0^  per  lb. 

The  costs  of  the  railway  tracks,  the  roadway  pavements  with  their  rein- 
forced-concrete  bases,  and  the  reinforced-concrete  sidewalks  have  been 
ignored  when  computing  the  total  costs  of  structures,  because  they  are 
common  to  the  two  classes  of  bridges  compared. 

In  making  the  computations  for  this  investigation,  the  avithor  took  the 
liberty  of  adopting  several  short  cuts,  such  as  assuming  squared  instead  of 
rounded  ends  for  all  piers,  using  generally  the  method  of  "end  areas" 
instead  of  that  of  the  "prismoidal  formula"  when  calculating  volumes  of 
masonry,  carrying  out  quantities  of  materials  and  total  costs  to  rather  large 
limiting  units,  and  estimating  costs  of  certain  parts  by  proportion  from  the 
previously-computed  costs  of  similar  parts  of  other  structui-es.  All  these 
and  many  other  short  cuts  for  avoiding  labor  are  perfectly  legitimate  when 
making  comparative  estimates,  provided  that  they  affect  alike  the  com- 
pared types  of  construction,  as  they  do  in  this  case. 

In  the  plotted  curves  of  the  accompanying  diagrams  no  curve  was 


ECONOMICS  OF  CANTILEVER  AND   SUSPENSION  BRIDGES  93 

drawn  through  less  than  three  located  points,  and  in  many  cases  the  num- 
ber was  four  or  more.  The  regularity  of  all  the  curves  proves  that  there 
was  no  error  of  any  magnitude  in  the  figuring  which  located  the  points 
thereof.  It  does  not  mean,  however,  that  the  author's  calculations  con- 
tained no  errors.  Unfortunately,  several  mistakes  crept  into  the  work, 
but  the  plotting  invariably  pointed  them  out  and  led  quickly  to  their 
satisfactory  correction. 

In  the  diagrams  the  abscissae  represent  main-span  lengths  in  feet,  and 
the  ordinates  show  the  total  costs  of  structures  in  dollars,  the  recorded 
units  being  milhons. 

In  figuring  the  weights  of  stiffening  trusses  for  suspension  bridges,  the 
author  made  an  important  modification  in  one  of  the  formulae  given  in 
Chapter  XXVII  of  "Bridge  Engineering."*  Equation  15  thereof  has  been 
employed  without  change,  when  wind  stresses  are  ignored;  but  the  follow- 
ing formula  for  the  weight  'per  foot  of  both  trusses  has  been  added  to  cover  the 
case  wliere  the  effect  of  the  wind  load  is  considered: 


The  corresponding  equation  when  the  wind  stresses  are  ignored  is : 

7^  =  2.8  5.06 


Mm  .  3.26F™/p2+2d2\ 


ds  s       \     dp     / 

The  greater  of  the  two  values  of  T  given  by  these  equations  is,  of  course, 
the  one  to  use  in  the  estimate  of  total  weight  of  metal. 

The  division  of  total  metal  weight  between  carbon  steel  and  nickel  steel 
was  made  by  the  author's  judgment,  based  upon  the  curves  in  his  two 
before-mentioned  papers  and  upon  the  assumptions  of  material  distribution 
adopted  when  preparing  the  suspension -bridge  computations.  No  error 
of  any  magnitude  exists  because  of  this  assumed  distribution,  although,  of 
course,  the  method  employed  is  only  approximately  correct. 

Whenever  a  proper  weight  curve  for  cantilever  structures  was  not 
available,  the  author  fell  back  upon  the  general  curves  for  weights  of  metal 
in  trusses  and  laterals  that  record  the  various  double-panel  weights  in  can- 
tilever arms  and  anchor  arms  as  multiples  of  the  corresponding  double- 
panel  weight  of  the  suspended  span,  which  general  curves  were  first  given  on 
Plate  X  of  "De  Pontibus,"  and  afterwards  were  reproduced  in  Fig.  25j 
of  "Bridge  Engineering." 

In  establishing  the  general  assumptions  for  the  layouts  of  both  canti- 
lever and  suspension  bridges,  with  one  exception  they  were  made  as  favor- 
able as  possible  for  each  type,  that  exception  being  that,  for  the  sake  of 
appearance,  the  anchor  arms  of  each  cantilever  structure  were  made  of  the 

*  This  modification  has  lately  been  incorporated  in  the  third  thousand  of  that 
treatise,  now  on  sale. 


04  ECONOMICS   OF  BRIDGEWORK  Chapter  XIII 

same  length  as  that  of  the  cantilever  arms,  viz. :  0.3125  of  the  main  opening, 
instead  of  the  more  economic  value  of  0.2  thereof.  Concerning  the  cor- 
rectness of  the  last  claim  for  economy  there  is  some  dispute  in  the  profes- 
sion; but  of  this  matter,  more  anon. 

In  the  suspension-bridge  layout  the  backstays  were  not  used  to  support 
side  spans,  but  were  run  by  approximately  right  hnes  to  the  anchorages. 
This  is  the  most  economic  layout  possible,  because  a  steel-trestle  approach 
is  always  cheaper  than  any  layout  of  truss  spans  that  can  be  made,  not 
only  because  it  requires  less  metal,  but  also  because  the  unit  prices  thereof 
erected  are  somewhat  smaller. 

The  main  piers  of  all  the  cantilever  bridges  and  most  of  those  for  the 
suspension  structures  were  designed  as  two  pedestals  with  a  reinforced- 
concrete  wall  between,  this  wall  extending  a  short  distance  below  extreme- 
low-water  mark.  It  was  found,  however,  in  the  case  of  the  combined 
four-track-railway-and-highway  suspension-bridges,  that  it  was  just  as 
economic  to  use  a  continuous  pier,  because  of  the  four  points  of  support 
required  by  the  tower  columns,  hence  that  feature  of  construction  was 
adopted. 

The  method  employed  for  finding  the  quantity  of  concrete  in  the 
anchor  pier  for  a  cantilever  bridge  was  to  compute  the  maximum  uplift, 
multiply  it  by  two,  and  divide  the  product  by  the  weight  of  one  cubic  foot 
of  concrete,  taking  due  cognizance,  of  course,  of  the  buoyant  effort  of  the 
water  on  all  submerged  portions  thereof.  If  the  volume  thus  found  would 
work  up  into  a  properly-shaped  pier,  well  and  good;  but  if  not,  an  addi- 
tional amount  was  provided. 

The  method  of  proportioning  the  anchorages  for  suspension  bridges, 
when  the  foundations  were  solid  rock,  was  to  make  each  one  quite  long  and 
narrow,  high  in  the  rear  and  low  in  the  front,  and  to  let  the  line  of  pressure 
reach  the  base  exactly  on  the  edge  of  the  middle  third  thereof.  In  case  the 
foundation  were  piles,  a  similar  shape  was  used,  but  it  was  necessary  to  keep 
the  load  on  each  pile  of  the  front  row  down  to  forty  tons. 

When  piles  were  employed  to  support  the  main  piers,  the  Hmiting 
load  per  pile  was  taken  also  at  forty  tons,  exclusive  of  the  effect  of  wind 
pressure.     The  piles  used  were  all  assumed  to  be  one  hundred  feet  long. 

The  limiting  widths  of  structure  were  as  follows:  In  cantilever  bridges 
one  twenty-fifth  of  the  main  opening;  in  suspension  bridges  one-twentieth 
thereof,  measuring  between  central  planes  of  exterior  columns  over  main 
piers;  and  between  central  planes  of  stiffening  trusses  one-thirtieth  of  the 
main  opening.  As  a  matter  of  economj^,  in  some  of  the  cantilever  struc- 
tures the  distance  between  truss  planes  was  made  as  small  as  practicable 
for  the  suspended  span,  and  was  gradually  widened  out  to  a  maximum  over 
the  main  ])ier,  and  then  gi'adually  re(hiced  to  a  mininuun  over  the  anchor 
pier. 

The  economic  lengths  for  the  cantilever  structui-c^s  were  taken  as  estab- 
lished tw(!iity  years  or  more  ago  by  the  autlu)r  wIumi  preparing  the  MS.  of 


ECONOMICS  OF  CANTILEVER  AND   SUSPENSION  BRIDGES 


95 


"De  Pontibus,"  viz.:  For  the  suspended  span,  three-eighths  of  the  main 
opening;  for  each  cantilever  arm,  five-sixteenths  of  the  main  opening.  As 
before  stated,  the  length  of  the  anchor  arm,  for  the  sake  of  appearance,  was 
made  the  same  as  that  of  .the  cantilever  arm,  although  some  metal  would 
have  been  saved  by  assuming  it  shorter. 

In  the  suspension  span,  also,  economic  dimensions  were  used,  viz.: 
one-fortieth  of  the  length  for  the  truss  depth,  and  one-ninth  thereof  for 
the  deflection  of  the  cables.  In  order  to  provide  proper  splay  for  the  latter 
(when  splay  was  required),  the  tower  width,  as  before  indicated,  was  made 
one-twentieth  of  the  main  opening.  This  militated  but  slightly  against  the 
suspension  bridge,  because,  in  the  substructure,  it  generally  increased  the 
cost  of  only  the  walls  between  the  pedestals  of  the  main  piers,  the  increase 
being  a  bagatelle  in  comparison  with  the  total  cost  of  the  said  substructure. 

The  first  estimates  prepared  by  the  author  were  for  double-track-rail- 
way bridges;  and  he  assumed,  to  begin  with,  an  opening  of  1,700  feet,  which 
is  approximately  Dr.  Steinman's  span-length  for  equal  cost.  The  profile 
adopted  for  this  crossing  is  shown  in  Fig.  13a  and  Fig.  136.     It  will  be  seen 


Fig.  13a.     Layout  for  1,700-foot  Span  Cantilever  Railway  Bridge. 


Fig.  136.     Layout  for  1,700-foot  Span  Suspension  Railway  Bridge. 

that  there  is  a  difference  of  twenty-five  feet  between  high  water  and  low 
water,  that  the  river  bed  is  some  fifty  feet  below  the  latter,  and  that  the 
bed  rock  is  one  hundred  feet  below  the  same  for  condition  No.  1.  In  con- 
dition No.  2  there  is  no  bed  rock,  hence  the  piers  and  anchorages  are  sup- 
ported on  piles.  As  the  author  had  anticipated,  the  result  of  the  calcula- 
tions showed  a  large  difference  in  favor  of  the  cantilever  structure,  the 


96 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XIII 


total  costs  being  $4,120,000  and  87,980,000.  These  figures  are  for  condi- 
tion No.  1,  in  wliich  all  piers  and  anchorages  were  assiuned  to  be  sunk  by 
the  pneimiatic  process  to  bed  rock. 


1700     1800      1900     2000      2100      ZZOO     2300     2m      2500     2600    270Q 
Afa/n  5pan-Lep<jfh  in  Fee/^ 

l''ici.  13c.     Cost  Curves  for  Double  Traek  Railway  Bridges. 

For  condition  No.  2,  in  which  there  is  no  bed  rock  within  reach  of  the 
piles,  the  corresponding  figures  were  $4,420,000  and  ,17,030,000. 

'11  ic  suspcnsion-bi'idge  anchorages  resting  on  piles  were  found  to  be  so 
much  clicapc'r  than  those  resting  on  bed  rock  that  it  was  concluded  to  adopt 
them  for  condition  No.  1,  and  to  assume  the  piles  to  be  driven  to  bed  rock. 


ECONOMICS  OF  CANTILEVER  AND   SUSPENSION  BRIDGES 


97 


In  order,  however,  to  make  the  comparison  perfectly  fair,  the  anchor-piers 
of  the  cantilever  bridge  were  also  figured  as  resting  on  piles  driven  to  bed 
rock.  The  result  of  this  change  was  a  large  reduction  of  the  difference  in 
cost  between  the  two  types  of  structure  compared,  as  shown  by  the  follow- 
ing totals:  $4,080,000  and  $6,387,000.  These  are  the  costs  which  are 
plotted  in  Fig.  13c. 

After  noting  the  large  difference  in  these  total  costs,  the  author  decided 
to  test  a  twenty-four-hundred-foot  opening,  thinking  that  surely  for  such 
a  long  span  the  suspension  bridge  would  be  the  cheaper.  The  bed  rock  was 
kept  at  the  same  elevation  as  before,  the  only  difference  in  the  profile  being 
that  the  width  of  river  was  increased,  as  shown  in  Fig.  13c/  and  Fig.  13e. 
It  was  decided,  in  order  to  save  labor,  to  do  no  further  computing  upon  the 
basis  of  main  piers  resting  on  piles;  but  all  anchor  piers  and  anchorages  were 
assumed  to  be  thus  supported,  as  in  the  final  estimates  for  the  1,700-foot 


Fig.  ISd.     Layout  for  2,400-foot  Span  Cantilever  Railway  Bridge. 

spans.  Much  to  the  author's  surprise,  the  results  showed  the  cantilever 
structure  to  be  still  the  cheaper,  the  total  costs  being  $10,210,000  and 
$12,033,000. 

Then  an  opening  of  twenty-seven  hundred  feet  was  tested,  the  result 
being  $15,269,000  for  the  cantilever  bridge  and  $15,259,000  for  the  suspen- 
sion bridge.  This  shows  that  for  double-track-railway  bridges  of  nickel 
steel,  the  span-length  for  equal  costs  of  cantilever  and  suspension  bridges  is 
2,700  feet,  or  one  hundred  feet  longer  than  the  greatest  advisable  length 
for  the  former  type  recommended  by  the  author  in  his  paper  on  "The 
Possibilities  in  Bridge  Construction  by  the  Use  of  High-Alloy  Steels." 

In  order  properly  to  plot  the  curves  in  Fig.  13c,  it  was  necessary  to 
compute  the  cost  of  a  cantilever  bridge  having  a  span  of  2,050  feet.  This 
gave  four  points  on  the  curve  and  enabled  it  to  be  sketched  in  satisfactorily, 
after  which  it  was  easy  to  draw  the  corresponding  curve  for  the  suspension 
bridge. 

In  order  to  make  as  good  a  showing  as  practicable  for  the  suspension 
bridge,  as  far  as  the  layout  is  concerned,,  it  v/as  decided  to  assume  that  the 
bed  rock  comes  quickly  to  the  surface  in  the  vicinity  of  the  main  piers  and 
runs  back  thereafter  at  an  elevation  of  about  ten  feet  above  high  water  in 
the  manner  adopted  by  Dr.  Steinman.     This  assumption  reduces  greatly 


98 


ECONOMICS    OF    BRIDGEWORK 


Chapter  XIII 


the  costs  of  the  anchorages  of  the  suspension  bridges  and  to  a  much  smaller 

extent  those  of  the  anchor  piers 
of  the  cantilever  structures.  The 
effect  of  this  change  on  the  cost 
curves  is  shown  in  Fig.  13/. 
From  it  there  will  be  observed 
that  the  span-length  for  equal 
cost  has  been  brought  down  to 
about  2,570  feet,  showing  that 
the  change  made  in  the  bed-rock 
profile  has  effected  comparatively 
little  variation  in  this  span-length. 

The  result  of  the  preceding 
calculations  differs  so  fundament- 
ally from  that  of  Dr.  Steinman 
that  the  author  found  it  neces- 
sary to  study  carefully  in  detail 
the  doctor's  various  assumptions 
and  estimates,  so  as  to  discover 
the  reason  or  reasons  for  the 
great  difference — amounting  to 
over  one  thousand  feet.  The 
following  variations  between  his 
data  and  estimates  as  compared 
with  those  of  the  author  were 
found:  . 

First.  In  his  cantilever 
bridges  Dr.  Steinman  makes  the 
ratio  of  length  of  suspended  span 
to  that  of  main  opening  vary 
from  0.5  for  1,000-foot  openings 
to  0.4  for  2,000-foot  openings, 
while  the  author  two  decades  ago 
showed  the  economic  ratio  to  be 
0.375;  and,  as  previously  men- 
tioned, he  (Dr.  Steimnan)  makes 
the  length  of  the  anchor  arm  0.4 
of  the  main  opening  instead  of 
about  one-half  of  that  amount. 

Second .  Dr.  S  t  e  i  n  m  a  n '  s 
bridges  carry  both  railway  and 
highway  live  loads,  while  the  au- 
thor's are  for  railway  traffic  only. 
Stciiiiii;iirs  susiK'iisioM  hiidges  have  side  spans  supported 
wliilc  in  I  he  aiillioi's  layouls  these  spans  are  replaced 


Third. 
by  tin;  bac 


ECONOMICS  OF  CANTILEVER  AND   SUSPENSION  BRIDGES 


99 


by    steel-trestle    approaches    entirely    disconnected    from     the     main 
structure. 

Fovrth.     Dr.  Steinman  uses  a  tension  intensity  of  worlcing  stress  of 
20,000  pounds  for  carbon  steel  and  one  of  30,000  pounds  for  nickel  steel, 


/XW    ISOO      /.eoo     2000     2/£»0     2.200    230O     2400     2500     26^  ^TdtO 

Fig.  13/.     Modified  Cost  Curves  for  Double  Track  Railway  Bridges. 

while  the  author's  practice  has  been  to  employ,  respectively,  16,000  pounds 
and  28,000  pounds. 

Fijth.  Dr.  Steinman  ignores  entirely  the  effect  of  impact  on  trusses, 
while  the  author  allows  for  it.  In  the  very  long  spans  this  cuts  but  little 
figure;  however,  such  is  not  the  case  for  the  shorter  spans. 


100  ECONOMICS   OF   BRIDGEWORK  Chapter  XIII 

Sixth.  Dr.  Steinman's  estimated  costs  for  substructure  not  only  exceed 
greatly  those  of  the  author,  buc  also  the  ratios  of  division  thereof  between 
main  piers  and  anchorages  are  fundamentally  different  from  liis. 

Seventh.  In  his  cantilever-bridge  estimates  Dr.  Steimnan  divides  the 
metal  into  five  groups,  viz.:  Suspended  span,  cantilever  arms,  anchor 
arms,  towers,  and  anchorages,  but  some  of  the  total  amounts  for  these 
groups  are  greatly  out  of  proportion. 

Eighth.  Dr.  Steinman  uses  an  intensity  of  working  stress  for  wire  cables 
varying  with  the  span  length,  while  the  author  has  employed  a  constant 
value,  in  accordance  with  his  standard  practice  of  varying  live  loads  and 
impact  allowances  and  keeping  the  unit  stresses  unchanged.  The  effect 
of  this  variation  would  be  to  shorten  somewhat  the  span-length  for  equal 
cost  of  the  contrasted  types. 

A  dissertation  upon  the  first,  sixth,  and  seventh  variations  may  throw 
some  light  upon  the  subject;  and,  to  make  it  properly,  it  became  necessary 
to  reproduce  here  Dr.  Steinman's  two  layouts,  as  shown  in  Fig.  13{/  and 
Fig.  13/i. 

Is  it  not  evident  from  a  glance  at  Fig.  13g  that  the  long  anchor  arms, 
passing  over  dry  land,  must  be  uneconomic  as  compared  with  steel  trestle- 
work,  which,  as  is  well  known,  is  the  cheapest  kind  of  metallic  structure? 
It  is  true  that  Dr.  Steinman,  Dr.  Burr,  and,  possibly,  other  writers  have 
shown  mathematically  that  the  economic  length  of  the  anchor  arm  is  four- 
tenths  of  the  main  opening;*  but  such  questions  cannot  be  solved  by  math- 
ematical analysis,  for  it  is  impracticable  to  consider  by  equations  the  many 
variables  in  the  make-up  of  an  anchor  arm,  as  well  as  simultaneously  a 
trestle  approach.  Dealing  with  this  point,  the  author  made  the  following 
statement  in  ''De  Pontibus":  ''When,  however,  the  problem  is  to  deter- 
mine the  economic  length  of  anchor  arm  for  a  fixed  distance  between  main 
piers,  the  result  will  be  quite  different;  because,  within  reasonable  limits, 
the  shorter  the  anchor  arm  the  smaller  will  be  its  total  weight  of  metal,  and 
because  trestle  approach  is  much  less  expensive  than  anchor  arm.  It  would 
not,  for  evident  reasons,  be  advisable  to  make  the  length  of  anchor  arm  less 
than  twenty  per  cent  of  that  of  the  main  opening,  or,  say,  fifteen  per  cent  of 
the  total  distance  between  centers  of  anchorages.  With  this  length  there 
would  probably  be  no  reversion  of  stress  in  the  chords  of  the  anchor  arm, 
even  when  impact  is  considered.  Generally,  though,  the  appearance  of  the 
structure  will  be  improved  by  using  longer  anchor  arms  than  the  inferior 
hmit." 

If  there  were  no  other  way  to  settle  this  question,  the  author  would  be 
willing  to  determine  it  beyond  all  possibility  of  doubt  by  preparing  actual 
designs  and  estimates  of  quantities  and  costs  for  the  anchor  arm  layout 

*  Thi.s  is  nearly  correct  for  the  (^:isc  where  the  locations  of  the  anchorages  are  fixed, 
\vhil(!  the  main  piers  may  he-  plnccil  ulicrc  (Icsiri'd;  !>ut  in  Dr.  Steinman's  study  it  is 
th(!  iriuin  piers  that  are  fixeil  in  location,  licncic  the  assumption  made  for  economic 
leiiKlli  of  aiiclior-arma  is  unwarranted. 


ECONOMICS  OF  CANTILEVER  AND   SUSPENSION  BRIDGES 


101 


of  Fig.  13(7,  and  for  a  corresponding  layout  in  which  the  exterior  half  thereof 
is  replaced  by  steel  trestle ;  but  as  this  would  involve  considerable  trouble 


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and  an  expense  amounting  to  several  hundreds  of  dollars,  the  following  a 
priori  observations  ought  to  be  sufficiently  convincing: 


102  ECONOMICS   OF   BEIDGEWOKK  Chapter  XIII 

First.  About  29  per  cent  of  the  total  weight  of  the  trusses  and  laterals 
of  this  anchor  arm  is  included  in  its  outer  haK,  and  the  average  weight  per 
foot  of  this  portion  is  about  71  per  cent  of  that  for  the  entire  structure. 
Applying  this  to  the  already  computed  weights  of  a  double-track-railway 
cantilever-bridge  having  a  1,500-foot  opening,  and  using  the  unit  costs  of 
materials  in  place  as  stated,  makes  the  average  value  per  linear  foot  of  the 
outer  haK  of  the  anchor  arm  $640.  The  weight  of  metal  per  hneal  foot  for 
a  double-track  steel-trestle  one  hundred  and  forty  feet  high  is  4,200  pounds 
and  its  value  is  $210,  to  which  should  be  added  not  to  exceed  $5  per  lineal 
foot  for  the  cheap  concrete  pedestals  required  to  raise  the  column  feet  a 
short  distance  above  the  rock  foundation.  This  shows  that  the  trestle 
costs  only  one-third  as  much  as  does  the  outer  half  of  the  anchor  arm. 

Second.  While  it  is  conceded  that  the  remaining  portion  of  the  anchor 
arm  may  weigh  somewhat  less  per  foot  than  it  would  as  an  independent 
arm,  the  difference  will  be  small  for  the  following  reasons: 

(a)  As  the  moment  over  the  pier  is  the  same  for  all  lengths  of  the 
anchor  arm  (because  it  comes  entirely  from  the  loadings  on  the  cantilever 
arm  and  the  suspended  span),  the  weights  of  metal  in  the  truss  members 
lying  near  the  pier  will  not  differ  greatly  in  the  two  cases. 

(b)  While  the  negative  stresses  due  to  the  uplift  will  be  increased  by 
the  halving  of  the  resisting  lever  arm,  on  the  other  hand  the  direct  live  load 
stresses  will  be  greatly  diminished  because  of  the  halving  of  the  span  length, 
these  two  effects  tending  to  offset  each  other. 

(c)  With  the  short  anchor  arm,  the  stresses  in  the  outer  diagonals  (as 
well  as  in  all  the  other  main  diagonals)  and  in  the  top  chord  members  will 
always  be  tensile,  hence  eye-bars  can  be  used  for  these  members,  thus 
effecting  a  great  saving;  because,  owing  to  the  increase  in  sectional  area  (to 
allow  for  rivet  holes)  and  to  the  weight  of  the  details,  it  takes  nearly  fifty 
per  cent  more  metal  to  build  a  riveted  tension  member  than  is  required  for 
the  corresponding  eye-bars  and  their  pins. 

(d)  While  it  is  true  that  the  short  arm  produces  a  greater  uplift  and, 
consequently,  necessitates  a  heavier  anchorage,  it  must  be  remembered 
that  the  value  of  an  economically -designed  anchor-pier  is  veiy  small  in 
comparison  with  the  cost  of  the  rest  of  the  structure.  Again,  it  must  not 
be  forgotten  that  with  the  long  arm  there  is  positive  as  well  as  negative 
loading  on  the  anchor  pier,  and  that,  in  consequence,  it  is  possible  that 
there  would  be  no  difference  worth  mentioning  in  the  costs  of  the  two  anchor 
piers. 

It  seems  to  the  author  that,  in  view  of  the  preceding,  it  ought  to  be 
evident  without  further  calculation  that  a  length  for  the  anchor  arm  equal 
to  two-tenths  of  the  opening  ought  to  be  decidedly  more  economic  than  a 
length  twice  as  great. 

In  respect  to  the  substructure,  Dr.  Steinman  in  his  design  for  his  1 ,500- 
foot-span,  four-track,  steam-rail way-and-highway,  cantilever  bridge^  found 
the  cost  of  two  main  piers  to  be  $1,202,000,  and  that  of  two  anchor  piers 


ECONOMICS  OF  CANTILEVER  AND   SUSPENSION  BRIDGES 


103 


$1,032,000;  while  the  author  found  for  his  nearest  corresponding  double- 
track,  steam-railway  bridge  $827,000  and  $161,000.  While  it  is  entirely 
impracticable  to  compare  these  figures,  because  of  fundamental  differences 
in  both  the  loading  and  the  foundation  conditions,  it  is  evident  that  Dr. 
Steinman  must  have  made  some  serious  mistake  in  his  calculations  when  he 
caused  the  costs  of  his  main  piers,  with  their  pneimiatic  foundations,  and 
his  anchor  piers,  resting  on  bare,  dry  bed-rock,  to  be  so  nearly  alike; 
because  the  latter  generally  are  insignificant  affairs  when  compared  with  the 
former.  This  same  error  exists  in  the  other  two  cantilever  bridges  which  he 
has  computed;  for  in  his  1,000-foot  span  he  found,  respectively,  $876,000 
and  $524,000,  and  in  his  2,000-foot  span  $2,153,000  and  $1,994,000.  This 
matter  will  receive  additional  attention  later  on. 

In  respect  to  his  division  of  weights  of  metal  in  superstructure.  Dr. 
Steinman  recorded  the  following: 

TABLE    137. 
Vv'eights  of  Metal  in  PorNDS 


Main 

Span 

in  Feet 

The 

Suspended 

Span 

Two 

Cantilever 

Arms 

Two 
Anchor 
Arms  . 

Two 

Towers 

Two 
Anchorages 

1,000 
1,500 
2,000 

8,738,000 
15,550,000 
28,964,000 

6,551,000 
16,951,000 
39,750,000 

9,697,000 
20,566,000 
42,851,000 

5,987,000 
17,479,000 
40,158,000 

785,000 
1,794,000 
3,374,000 

Referring  to  the  item  of  weight  of  the  towers  in  both  the  1,500-foot-span 
and  the  2,000-foot-span  structures  it  exceeds  the  total  weight  of  metal  in  the 
cantilever  arms,  and  is  but  little  less  than  that  in  the  excessively-long  anchor 
arms.  Surely  this  cannot  be  correct!  Each  tower  consists  of  two  braced 
columns,  the  oad  on  each  of  which  is  composed  of  the  vertical  components 
of  the  stresses  in  the  two  upper-chord  members  meeting  at  its  top,  and  these 
are  not  extraordinarily  great.  Had  the  upper  chords  been  run  horizontally 
from  inner  hip  to  inner  hip,  the  column  stresses  would  have  been  zero,  bar- 
ring those  due  to  their  own  weight  and  to  an  insignificant  wind  pressure  on 
the  columns  themselves  only. 

Such  glaringly -great  irregularities  as  these  upset  the  entire  economic 
comparison  and  render  its  results  woithless.  Moreover,  all  these  variations 
from  correctness  combine  to  militate  against  the  cantilever  structure. 
On  the  other  hand,  though,  the  assumption  of  side  spans  supported  by  the 
backstays  militates  against  the  suspension  structure. 

In  view  of  the  preceding,  the  author  concluded  that  it  would  be  neces- 
sary to  compute  quantities  and  plot  cost  curves  for  cantilever  and  sus- 
pension bridges  of  the  type  and  loading  assumed  by  Dr.  Steinman,  adhering 
as  closely  as  practicable  to  his  general  features  of  layout,  character  of  metal 
used  in  the  various  parts,  weights  per  foot  of  floor  systems  and  lateral  sys- 


104 


ECONOMICS    OF   BRIDGEWORK 


Chapter  XIII 


terns,  and  cost  per  foot  of  trestle  approaches;  but  differing  with  him  in  the 
following  particulars : 

First.  Raising  the  grade  of  the  structure  so  as  to  afford  a  vertical  clear= 
ance  of  150  feet  above  high  water,  and  lowering  the  elevation  of  main  pier 
foundations  to  35  feet  below  low  water.  This  is  more  in  accordance  with 
probable  actual  conditions  than  is  indicated  by  the  profile  in  Fig.  13g. 

Second.  Substituting  steel-trestle  approaches  for  the  side  spans  shown 
in  Fig.  13/i. 

Third.  Adopting  the  most  economical  type  of  substructure  for  each 
case. 

Fourth.  Adopting  a  length  of  anchor  arm  equal  to  5/16  L  instead  of 
0.4  L. 

With  these  premises  the  author  computed  the  costs  of  cantilever  and 
suspension  bridges  for  openings  of  1,500  feet  and  2,400  feet,  and  found  that 
the  span  of  equal  cost  lies  between  these  limits.  Then  he  figured  for  a 
2,000-foot  span.  This  gave  him  three  points  on  each  curve,  as  shown  in 
Fig.  13i,  besides  which,  he  estimated  in  detail  bj^  proportion  the  costs  for 
several  other  openings  and  plotted  the  results  of  these  also.  Fig.  13t 
shows  that  the  syjan-length  for  equal  cost  is  about  2,190  feet,  instead  of  the 
1,670  feet  found  by  Dr.  Steimnan — a  difference  of  over  500  feet. 

It  will  be  interesting  to  compare  the  substructure  costs  found  by  Dr. 
Steinman  and  those  found  by  the  author  for  like  spans  and  practically  the 
same  general  conditions,  as  recorded  in  the  following  table: 

TABLE    136 


Main  Siian-length  and 

Cost  in  Dollars  of  the 
Main  Piers 

Cost  in  Dollars  of  the 
Anchorages 

Character  of  Structure 

Steinman 

Waddell 

Steinman 

Waddell 

1,000-foot  Cantilever 

1,500-foot  Cantilever 

876,000 
1,262,000 
1,330,000 
2,153,000 

524,000 
1,032,000 
2,428,000 
1,944,000 

506,000 
440,000 
660,000 
600,000 

290,000 

1,500-foot  Suspension 

2,000-foot  Cantilever 

2,000-foot  Suspension 

1,222,000 

310,000 

1,920,000 

2,250-foot  Suspension 

1,835,000 

4,174,000 

2,400-fo()t  Cantilever 

926,000 
880,000 

357,000 

2,400-fof)t  Sus[)ension 

2,400,000 

3,000-f(K>t  Suspension 

3,017,000 

6,995,000 

Of  the  preceding  nine  cases  there  are  only  three  which  can  be  directly 
compared,  viz.,  the  1,500-foot  cantilcvcM-,  llio  1,500-foot  suspension,  and  the 
2,000-r()()t  cantilever,  although  ollu-r  coniiKU'isons  miglit  be  made  ai)iii"oxi- 
malely  by  inter])()lation.  It  will  \)v  iH)(i('(>d  (hat  Dr.  Steinman's  main  piers 
cost  two  or  three  times  as  much  as  those  of  [\\v  author,  his  anchor  piers  for 


ECONOMICS   OF   CANTILEVER  AND   SUSPENSION   BRIDGES  105 


cantilevers  from  three  and  a  half  to  six  times  as  nnich,  and  his  anchorages 
for  suspension  bridges  about  twice  as  much.  This  gives  further  proof  of  the 
statement  previously  made  to  the  effect  that  his  entire  economic  investiga- 


/4a>  /sao     /£>M 


Z2PO    ?9M    ;3Vft» 


Fig.  13i. 


nao    /e^    /m>    zaoo   z/oo 
/^m  S/x3/?-l&^^  iff  f^'f^ 

Cost  Curves  for  Combined  Railway  and  Highway  Bridges  of  the  General 
Type  Computed  by  Dr.  Steinman. 


tion  is  incorrect  and  that  the  deduction  which  he  makes  therefrom  concern- 
ing the  span  length  for  equal  cost  is  wrong. 

In  thus  criticizing  Dr.  Steinman's  little  book,  the  author  does  so  merely 
because  he  feels  that  the  profession  should  not  be  left  in  error  on  such  an 


106  ECONOMICS   OF   BRIDGEWORK  Chapter  XIII 

important  point  as  the  comparative  economics  of  cantilever  and  suspension 
bridges.  Some  time  in  the  not  very  distant  future  there  are  going  to  be 
built  in  this  country  many  long-span  bridges;  and  it  behooves  engineers  to 
know  in  advance  the  economics  of  the  different  types  of  structures  appli- 
cable thereto.  Dr.  Steinman  deserv^es  great  credit  for  his  energ;^^  and 
courage  in  attacking  such  a  stupendous  problem  at  such  an  early  date  in 
his  professional  career,  without  -any  records  of  weights  at  his  disposal,  and 
before  he  had  had  any  actual  experience  in  bridgework.  In  undertaking 
such  an  immense  task  he  set  a  splendid  example  to  other  young  engineers; 
and  the  incorrectness  of  his  conclusion  is  no  blot  whatsoever  upon  his  pro- 
fessional record.  It  would  be  well  for  engineering  if  there  were  in  its  ranks 
many  more  young  men  possessing  the  attributes  of  energy,  ambition,  and 
love  for  hard  work  to  the  same  extent  that  he  does.  Such  men  will  be 
badly  needed  in  every  branch  of  technics,  if  our  profession  is  to  take  the 
high  position  in  the  community  to  which  it  is  entitled  by  its  importance  to 
mankind. 

Dr.  Steinman  can  console  himseK  with  the  reflection  that  he  is  not  the 
only  engineer  who  has  devoted  an  entire  treatise  to  the  production  of  a 
wrong  conclusion,  for  several  decades  ago  an  eminent  French  professor  of 
engineering  published  a  large  book  deahng  with  the  economics  of  truss 
bridges,  basing  his  calculations  upon  such  incorrect  premises  that  the 
result  of  his  work  was  of  no  real  value  to  the  profession. 

Comparing  the  results  of  the  preceding  calculations,  as  shown  in  Fig. 
13c  and  Fig.  13i,  it  will  be  noticed  that  the  span  length  for  equal  cost  is 
much  less  for  the  combined  railway  and  highway  type  of  structure  than  for 
the  strictly  railway  type.  The  reason  for  this  is  that  in  a  modern  highway 
bridge  the  proportion  of  dead  load  to  live  load  is  much  greater  than  it  is  in  a 
railway  bridge,  because  of  the  large  weight  of  the  pavement,  the  supporting 
slabs,  and  the  concrete  footwalks.  In  the  stiffening  trusses  of  a  suspension 
bridge  it  is  generally  the  live  load  only  which  causes  stresses  that  influence 
the  sectional  areas  of  the  members,  the  dead  load  having  no  effect  thereon 
whatsoever,  but  in  a  cantilever  bridge  it  is  the  total  live  load  plus  the  dead 
load  which  does  so,  with  sometimes  a  little  assistance  from  the  wind  load; 
hence  it  is  evident  that  the  smaller  the  i)roportion  of  live  load  to  total  load 
the  more  favorable  it  is  for  the  susp(;nsion  bridge.  On  this  account,  in 
strictly  highway  structures,  the  span  length  for  equal  cost  will  be  much 
shoi'ler  than  those  thus  far  determined.  Not  knowing  what  the  length 
would  probably  be,  the  author  hgured  the  costs  of  the  two  types  for  1,500- 
foot,  1,200-foot,  and  1,000-foot  main  openings,  using  carbon  steel  only; 
and  fi-()rn  the  i-esults  of  the  computations  lie  plotted  the  curves  in  Fig.  13^. 
From  this  diagram  it  will  be  seen  that  the  span  length  for  equal  cost  is 
about  1,000  feet. 

Recognizing  that  this  investigatioTi  would  not  l)e  comiilete  without 
pr(!paring  a  set  of  coinj^iitalions  for  slrictly-highway  structures  of  nickel 
steel,  the  necessary  calculations  were  made  for  a  1,000-foot  span  of  each 


ECONOMICS   OF  CANTILEVER  AND   SUSPENSION  BRIDGES         107 


type,  the  result  showing  ahnost  exactly  equnl  costs.  This  indicates  that 
the  strength  of  the  steel  used  does  not  modify  the  span  length  for  equal 
cost  in  highway  structures,  although  changing  the  totals  of  the  estimates. 


//a:?  /Jtv  /3aff 

Fig.  13j.     Cost  Curves  for  Highway  Bridges  of  Carbon  Steel. 


These  highway  bridges  are  of  the  same  kind  as  that  adopted  as  standard 
by  the  author  in  his  late  paper  on  "The  Economics  of  Steel  Arch  Bridges," 
viz.,  a  deck  about  60  feet  wide,  out  to  out,  composed  of  a  paved  roadway 
42  feet  wide,  resting  on  a  reinforced-concrete  base,  and  having  a  double- 
track  street-railway  at  the  middle,  and  two  8-foot-wide,  reinforced-concrete 


108  ECONOMICS   OF   BRIDGE  WORK  Chapter  XIII 

sidewalks.  The  live  loads  for  the  floor  sj^stem  are  Class  25  for  the  electric 
railway,  Class  B  for  the  rest  of  the  roadway,  and  Class  C  for  the  side- 
walks.    Class  A  over  the  full  width  of  the  deck  was  employed  for  the  trusses. 

RESUME   OF   INVESTIGATION 

First.  For  exclusively  railroad  bridges,  the  economic  limit  for  the 
cantilever  type  of  structure,  or,  m  other  words,  the  mam  span  length  for  a 
cost  equal  to  that  of  the  corresponding  suspension  bridge  is  that  length 
which  requhes  4|  pounds  of  metal  to  carry  1  pound  of  live  load. 

Second.  For  modern  highway  structures,  carrying  also  incidentally 
electric  railway  tracks,  this  span' length  for  equal  cost  is  1,000  feet. 

Third.  For  combined-railway-and-highway  structures  the  hmit  is 
intermediate  between  the  limit  for  railway  structures  and  that  for  high- 
way .structures,  the  interpolation  being  done  in  direct  proportion  to  the 
ratio  of  railway-truss-live-load  to  total-truss-live-load. 

This  may  be  expressed  by  formula  thus:  If  G  is  the  span  length  of 
equal  cost  for  strictly-railway  bridges,  and  R  is  the  ratio  of  railway-tiuss- 
hve-load  to  total-truss-live-load,  then,  for  combined-railway-and-highway 
structures  the  span  length  for  equal  cost  will  be  given  approximately  by 
the  equation: 

,S,=  1,000+ (G- 1, 000) /? 

For  instance,  if  (7=2,700  feet  for  nickel  steel  railway  bridges  and  i2  =  |, 

S,=  1,000+1,700x1  =  2,133 

This  checks  fairly  well  with  the  value  shown  in  Fig.  13t,   where 

12,000  _  2 
"18,000  "3* 

Fig.  13/i  is  a  diagram  from  which  can  be  found  at  a  glance  the  span 
length  for  ofjual  cost  for  any  proportionate  combination  of  railway  and 
highway  live  loads,  under  the  assumption  that  nickel  steel  is  employed 
for  the  principal  portions  of  the  structure.  In  case,  though,  that  carbon 
steel  alone  be  used,  which  is  unlikely,  the  limiting  span  length  for  canti- 
lever construction  is  to  be  taken  at  about  2,000  feet. 

Whil(>,  it  was  not  intended  to  do  any  figuring  concerning  the  com- 
pai-ativ(!  economics  of  cantilever  and  suspension  bridges  when  alloy  steels 
having  higher  elastic  limits  than  60,000  pounds  per  square  inch  are  cm- 
ploy  (m1,  it  was  surmised  that  the  span  Icngtli  for  equal  cost  for  strictly- 
railway  bridges  will  not  differ  essentially  from  the  limiting  lengths  for 
cantilever  main  spans  determined  by  the  author  in  "The  Possibilities  in 
liiidg(!  (Construction  })y  the  Use  of  High  Alloy  Steels,"  viz.: 

For  E=   70,000  pounds  per  square  inch 2,780  feet 

For  Fj=   8(),(K)()  i)oun(ls  ])er  square  inch 2,910  feet 

For  Fj=  0(),0()()  i)oun(ls  per  square  inch 3,030  feet 

For  ^=100,000  pounds  per  square  inch 3,140  feet 


ECONOMICS  OF  CANTILEVER  AND  SUSPENSION  BRIDGES 


109 


It  is  possible  that  the  author  is  not  entirely  justified  in  making  this 
surmise,  because  computations  might  show  that  the  span  length  for  equal 
cost  does  not  exceed  2,700  feet,  no  matter  how  high  may  be  the  alloy  of 
steel  used.     It  seemed  hardly  worth  while  to  spend  much  time  in  figuring 


<?«/<?«  Ct3  -i^  eS  4*  ^T  AS    ..j^  t9  „ 

£y//iife>f£iT//i^S!]yL'y&l^>a^/^rL/hea//w^^lSij/LV£loaaf/i^ 

Fig.  IS/b.     Diagram  of  Main  Span  Lengths  of  Equal  Cost  for  Combined  Railway 
and  Highway  Cantilever  and  Suspension  Bridges. 

upon  this  question  before  a  high  alloy  of  steel  satisfactory  for  long-span- 
bridge  building  is  found;  nevertheless,  as  a  matter  of  curiosity,  it  was 
decided  to  test  a  main  span  length  of  2,900  feet,  for  steel  having  an  elastic 
limit  of  80,000  pounds  per  square  inch,  and  assuming  that  the  cost  of  that 
metal  in  place  is  9  cents  per  pound. 


110  ECONOMICS    OF   BEIDGEWORK  Chapter  XIII 

The  comparative  figures  of  cost  for  the  two  structures  proved  to  be  as 
follows: 

Cantilever  bridge $15,720,000 

Suspension  bridge 15,233,000 

However,  had  the  price  of  the  alloy  steel  been  taken  at  8  cents  per  pound 
the  same  as  for  nickel  steel,  the  cost  estimates  would  have  been  as  follows: 

Cantilever  bridge $14,448,000 

Suspension  bridge 14,856,000 

As  these  last  figures  reverse  the  previously  found  economics  of  the  two 
types,  it  is  evident  that  for  bridges  of  high-alloy  steels  the  span  length 
for  equal  cost  is  vitally  dependent  upon  the  pound  price  of  the  said  aUoy 
steel,  the  lower  it  is  the  more  favorable  is  it  to  the  cantilever  structure. 
In  view  of  the  fact  that  at  present  no  one  has  any  idea  of  what  the  cost 
per  pound  wiU  be  for  high-alloy  steels  used  in  future  long-span-bridge 
construction,  it  will  be  well  to  adopt  temporarily  as  correct  the  author's 
before-mentioned  surmise,  viz.,  that  in  alloy  steel  bridges  carrying  railway 
loads  only,  the  span  length  for  equal  cost  is  that  for  which,  in  the  can- 
tilever bridge,  there  are  required  4|  pounds  of  metal  to  sustain  1  pound  of 
live  load. 

The  author  recognizes  that  a  change  in  the  assumed  conditions  would 
modify  somewhat  all  the  previously  found  span-lengths  of  equal  cost  for 
both  carbon-steel  and  nickel-steel  bridges;  but  he  does  not  believe  that 
the  variation  will  be  material — say  not  to  exceed  2  or  3  per  cent  in  any 
case  for  any  one  fundamental  change,  or  5  per  cent  for  any  probable  com- 
bination of  changes.  For  instance,  if  the  main  piers  rest  on  piles  instead 
of  going  to  bed  rock,  this  will  mihtate  a  little  against  the  suspension  struc- 
ture, increasing  slightly  the  span  length  for  equal  cost.  The  same  effect 
occurs  if  the  pound  price  for  steel  cables  be  increased  without  changing 
the  pound  prices  for  the  other  metals,  and  vice  versa. 

If  the  unit  prices  for  substructure  be  decreased,  the  result  will  be 
favorable  to  the  suspension  bridge,  because,  while  the  main  piers  will  be 
affected  about  alike,  there  will  be  a  greater  saving  in  the  anchorages  of  the 
suspension  bridge  than  in  the  anchor  piers  of  the  cantilever  structure. 
Let  us  see  what  effect  it  would  have  to  reduce  the  prices  of  all  concrete 
work  five  dollars  per  cubic  yard,  thus  bringing  them  close  to  the  lowest 
limits  for  truly-first-class  construction  that  have  existed  in  periods  of 
national  depression. 

In  the  railroad  bridges  of  2,700  feet  span,  the  reduction  in  total  cost  of 
substructure  would  be  $473,000  for  the  cantilever  bridge  and  $928,000  for 
the  suspension  bridge,  making  the  total  costs,  respectively,  $14,796,000 
and  $14,330,000.  Performing  the  corresponding  reduction  in  prices  of 
substructure  for  the  2,400-foot  spans  gives,  for  the  total  costs,  respectively, 
$9,877,000  and   $11,196,000.     Plotting  these  points  on   a   cross-section 


ECONOMICS   OF   CANTILEVER  AND   SUSPENSION  BRIDGES  111 

diagram  and  joining  them  properly  by  very  slightly  curved  lines  shows 
that  the  span  length  of  equal  cost  is  reduced  from  2,700  feet  to  2,640  feet. 
This  is  no  material  amount,  indicating,  as  it  does,  a  variation  of  only 
2.2  per  cent. 

Addendum 

The  preceding  was  written  in  the  summer  of  1918.  A  year  later  the 
author  was  called  in  by  some  prominent  citizens  of  Detroit  to  make  a 
study  of  the  governing  conditions  for  a  proposed  highway-and-street- 
railway  bridge  over  the  Detroit  River,  practically  on  a  line  joining  the 
business  centers  of  the  cities  of  Detroit  and  Windsor,  and  to  determine 
upon  the  best  type  of  structure  to  adopt.  A  few  days  of  investigation 
led  to  the  conclusion  that  a  single  span  of  2,500  feet,  crossing  the  entire 
river  in  the  clear  between  harbor  lines,  would  be  obligatory;  and,  accord- 
ingly, the  layout  and  the  approximate  cost-calculations  were  made  for  a 
suspension  bridge.  It  became  necessary  to  obtain  pound  prices  for 
structural  metal  (both  nickel  steel  and  carbon  steel)  and  wire  cables  in 
place;  and  the  following  values  were  found: 

Carbon  steel  erected 7.0^  per  lb. 

Nickel  steel  erected .  .  . 9.0^  per  lb. 

Cables  erected 23.0^  per  lb. 

The  last  figure  was  simply  staggering!  Surely,  such  an  enormous 
price  can  be  only  temporary,  for  the  great  difference  between  it  and  the 
other  two  figures  is  altogether  illogical.  Nevertheless,  it  shows  the  pos- 
sibility of  an  abnormal  price-condition  existing  long  enough  to  affect  tem- 
porarily the  economics  of  cantilever  and  suspension  bridges.  It  is  not 
likely  that  there  can  ever  be  a  worse  condition  than  the  one  at  present 
governing;  consequently,  the  author  has  recast  for  existing  unit  prices 
the  estimates  of  cost  made  for  the  preceding  investigation,  and  has  found 
the  following  results: 

The  span  of  equal  cost  for  highway  bridges  has  been  advanced  from 
1,000  feet  to  exactly  1,200  feet;  that  for  the  particular  combined  bridges 
investigated  has  been  increased  by  170  feet;  but  that  for  the  steam 
railway  bridges  has  been  augmented  only  60  feet.  The  reason  for  the 
smaller  increase  in  the  last  case  is  that,  in  cantilever  structures  the  weight 
curves,  and  consequently  the  cost  curves,  rise  very  rapidly  at  a  span  of 
2,700  feet,  because  such  a  length  is  really  a  little  beyond  the  truly  prac- 
ticable limit  for  that  style  of  bridge. 

These  variations  are  somewhat  greater  than  the  maximum  which  the 
author  anticipated  when  writing  his  paper;  but  at  that  time  he  never  would 
have  deemed  it  possible  that  such  a  great  variation  in  unit  prices  of  struc- 
tural steel  and  wire  cables  could  hold  as  that  which  exists  to-day;  nor 
does  he  now  consider  it  possible  that  it  can  be  made  to  last  for  any  great 
length  of  time. 


112  ECONOMICS   OF   BRIDGE  WORK  Chapter  XIII 

In  making  the  Detroit-Windsor  Bridge  study,  a  practical  proof  was 
given  of  the  usefulness  of  the  paper.  No  copy  of  "Bridge  Engineering" 
was  available  for  making  an  estimate  of  the  cost  of  the  suspension  bridge 
and  its  approaches,  but  a  copy  of  the  paper  was  at  hand ;  and,  as  a  rough 
estimate  was  required  immediately,  the  following  procedure  was  adopted, 
it  being  recognized  at  the  outset  that  all  the  assumptions  made  therein 
were  upon  the  side  of  safety,  and  that,  consequently,  the  resulting  figures 
of  cost  would  be  somewhat  too  great: 

Referring  to  Fig.  13 j,  the  curve  for  costs  of  suspension  bridges  was 
extended  on  an  enlarged  cross-section  sheet  to  a  span  of  1,700  feet,  at 
which  length  the  spans  on  Fig.  13c  begin.  Ths  cost  thus  found  was  mul- 
tiplied by  the  ratio  of  the  total  combined  clear  widths  of  roadway  and  side- 
walks for  the  two  structures  considered,  and  the  product  was  multiplied 
by  the  average  of  the  ratios  of  the  unit  costs  of  all  substructure  and 
superstructure  materials  in  place  for  present  conditions  and  the  condi- 
tions assumed  in  the  paper.  Then,  referring  to  Fig.  13c,  it  was  noted 
that  the  cost  of  a  2,500  foot-span  suspension-bridge  and  its  approaches 
is  almost  exactly  double  that  for  a  similar  1,700-foot  span  with  its 
approaches;  hence  the  cost  just  found  was  doubled,  and  to  the  result 
were  added  the  cost  of  the  entire  flooring  from  entrance  to  exit  of  structure, 
an  allowance  for  the  greater  length  of  the  approaches  involved,  and  the 
approximate  cost  of  either  elevators  or  an  escalator  and  a  stanway  at  the 
Detroit  approach. 

Later,  a  more  exact  estimate  of  cost  was  made  from  the  various  data  in 
"Bridge  Engineering,"  the  result  being  some  5  per  cent  less  than  that  of 
the  first  approximation.  This  more-exact  estimate  was  computed  in  a 
single  working  day.  Without  the  aid  of  the  book  mentioned,  it  would 
probably  have  required  as  many  weeks  of  figuring  as  it  actual^  took  hours 
thereof,  in  order  to  obtain  results  of  equal  accuracy. 

In  the  Appendix  to  the  original  paper  there  are  given  five  pages  of 
estimates  of  cost,  covering  fourteen  structures  out  of  the  twenty-five  that 
were  computed.  It  has  not  been  deemed  worth  while  to  reproduce  them 
in  this  treatise;  for  probably  they  would  not  be  of  much  interest  to  any 
reader.  If,  though,  anyone  desires  to  see  them,  he  can  do  so  by  consulting 
the  Transactions  of  the  Western  Society  of  Engineers. 


CHAPTER  XIV 

ECONOMICS    OF   BRIDGE   APPROACHES 

The  economics  of  approaches  to  bridges  will  involve  the  question 
whether  it  is  best  and  cheapest  to  build  earth  embankments,  timber  trestles, 
steel  viaducts,  reinforced-concrete  viaducts,  or  any  combination  of  these, 
and  at  what  heights  it  would  pay  to  change  from  one  type  of  construction 
to  another. 

In  determining  the  economics  of  the  different  kinds  of  structure  it 
does  not  suffice  to  compare  merely  their  first  costs;  for  it  is  necessary  to 
take  into  account  the  items  of  depreciation,  maintenance,  and  repairs  by 
computing  the  annual  expenses  for  these,  finding  the  sums  of  money 
which,  at  the  governing  rate  for  simple  interest,  would  produce  these 
annual  amounts,  and  adding  the  results  to  the  first  costs. 

In  certain  cases  it  might  not  be  best  to  adopt  the  theoretically-economic 
kind  of  structure,  because  the  requisite  funds  for  building  it  may  not  be 
available;  and  in  such  cases  the  cost  of  renewals  should  receive  due  con- 
sideration by  taking  cognizance  of  the  probable  increase  in  the  future 
prices  of  perishable  materials,  such  as  timber,  as  well  as  of  the  special 
danger  to  the  structure  from  fire  or  washout  due  to  the  employment,  either 
permanently  or  temporarily,  of  such  inferior  construction.  As  indicated 
in  a  previous  chapter,  the  danger  from  fire  to  a  structure  built  either 
wholly  or  partially  of  timber  is  a  serious  matter.  It  may  be  permissible 
under  certain  conditions  to  risk  losing  an  approach  to  a  bridge  by  either 
fire  or  flood;  but  if  the  danger  extends  also  to  the  main  structure,  the 
cheapening  expedient  is  not  permissible. 

Again,  due  consideration  should  be  given  to  the  question  of  the  expense 
caused  by  the  interruption  of  traffic  by  putting  out  of  commission  either 
one  or  both  of  the  approaches.  Generally  speaking,  it  does  not  pay  to 
take  any  chance  of  even  temporary  disaster  to  the  structure;  but,  as 
before  pointed  out,  it  sometimes  appears  to  be  unavoidable. 

In  the  case  of  embankments  when  earth  is  expensive  at  the  outset  and 
can  be  brought  to  the  site  much  more  cheaply  after  the  bridge  is  finished 
and  the  railroad  line  that  it  carries  is  in  operation,  it  will  generally  pay 
to  build,  as  inexpensively  as  possible,  a  timber  trestle;  and  later,  just 
before  it  begins  to  need  expensive  repairs,  fill  around  it  and  construct  an 
embankment  by  dumping  earth  from  above  by  means  of  a  construction 
train. 

113 


114  ECONOMICS   OF   BRIDGEWORK  Chapter  XIV 

There  is  an  economic  question  concerning  embankments,  not  at  all 
difficult  to  settle,  which  exists  when  the  right-of-way  is  expensive;  and 
that  is  whether  it  is  preferable  to  use  wide  banks  with  the  natural  side- 
slopes  or  to  build  concrete  side-walls  and  thus  diminish  the  area  to  be 
occupied.  The  only  proper  way  to  detennine  the  economics  in  this  case 
is  to  make  a  complete  estimate  of  cost  for  each  layout,  based  upon  current 
prices  of  materials,  labor,  and  right-of-way. 

Occasionally  in  an  engineer's  practice  there  arises  the  economic  ques- 
tion whether  it  will  be  better  to  build  an  expensive  abutment  with  wing- 
walls,  and  possibly  also  toe-walls,  or  an  inexpensive  buried  pier  with  longer 
superstructure  and  with  rip-rap  protection  along  the  end  and  sides  of  the 
embankment.  In  most  cases  the  latter  will  prove  the  more  economic, 
but  that  such  is  the  case  should  never  be  assumed  without  making  accurate 
comparative  estimates.  With  substantial  bank  protection  that  no  flood 
is  hkely  to  wash  out,  the  expedient  of  the  buried  pier  is  a  perfectly  legiti- 
mate one,  and  the  construction  invol  ^ed  by  its  use  can  properly  be  deemed 
first-class. 

The  choice  between  a  steel  trestle  and  a  reinforced-concrete  trestle  for 
an  approach  should  always  be  determined  by  including  in  the  comparing 
estimates  of  cost  the  equivalents  for  depreciation,  maintenance  and 
repairs,  giving  a  substantial  preference  to  the  concrete  layout  because  of 
the  possibility  of  future  deterioration  of  the  steel  due  to  neglect  of  painting. 

As  indicated  on  page  1193  of  "Bridge  Engineering"  there  are  given  in 
Chapters  53,  55,  and  56  of  that  treatise  a  large  number  of  tables  and  dia- 
grams, by  means  of  which  can  be  quickly  computed  the  costs  of  the  em- 
bankments, timber  trestles,  steel  viaducts,  reinforced-concrete  viaducts, 
retaining  walls,  abutments,  and  culverts  which  may  be  needed  in  esti- 
mating the  cost  of  approaches  to  bridges.  From  these  data  there  can  also 
be  found  very  easily  the  comparative  economics  of  plain  and  reinforced 
concrete  for  building  retaining  walls  and  abutments. 

It  is  sometimes  the  case  that  in  the  approaches  to  a  proposed  bridge 
there  would  be  a  variation  in  the  total  cost  of  right-of-way  and  property 
damages  by  adopting  different  kinds  of  construction  therefor,  hence 
this  matter  should  always  receive  due  consideration.  One  of  the  most 
effective  methods  of  economizing  on  these  items  is  to  substitute  a  spiral 
approach,  such  as  mentioned  on  page  1076  of  "Bridge  Engineering,"  for  the 
usual  straight  trestle.  While  the  construction  costs  of  the  two  types  do 
not  differ  materially,  if  the  property  occupied  or  damaged  be  very  valuable, 
a  great  saving  can  sometimes  be  secured  because  of  the  comparatively 
small  and  compact  area  required  for  the  spiral.  Moreover,  it  is  some- 
times practicable  to  construct  a  building  in  connection  with  the  latter, 
that  will  bring  in  such  large  rentals  as  more  than  to  wipe  out  all  costs  for 
right-of-way  and  property  damages. 

In  gcnei-al.  it  may  be  stated  that  timber  trestle  is  the  cheapest  kind  of 
approach,  as  far  as  first  cost  is  concei'ned,  excepting  for  small  heights,  but 


ECONOMICS   OF   BRIDGE   APPROACHES  115 

that  its  upkeep  and  replacement  are  expensive.  If  funds  for  the  con- 
struction are  hmited,  it  may  be  best  to  adopt  timber  trestle-work  in  spite 
of  its  being  ultimately  uneconomic,  with  the  expectation  of  saving  from  the 
traffic  receipts  enough  money  to  substitute  later  on,  when  replacement 
becomes  necessary,  the  most  desirable  type  of  construction. 

Of  the  permanent  types  of  approach,  the  embankment  is  the  cheapest 
where  the  property-cost  is  little  or  nothing,  excepting  when  the  grade  line 
is  very  high  or  the  earth  difficult  to  obtain  and,  therefore,  expensive. 

When  property  is  costly  or  side  slopes  are  not  permitted,  it  is  economic 
for  comparatively-low  grade-levels  to  adopt  earth  embankment  between 
retaining  walls. 

As  the  height  increases,  it  becomes  cheaper  to  pass  from  embankment 
to  trestlework ;  and  the  point  of  division  is  not  difficult  to  determine  when 
there  are  no  side  walls,  but  when  these  are  requisite,  it  will  be  necessary, 
as  previously  mentioned,  to  make  the  determination  by  actual  cost- 
estimates.  The  wider  the  approach  is  at  grade  surface,  the  greater,  for 
economy,  will  be  the  limiting  height  of  embankment. 

For  low  trestles  of  permanent  construction,  reinforced-concrete  wiU 
generally  prove  economic,  but  for  high  ones  it  will,  be  found  necessary  to 
employ  steel. 


CHAPTER  XV 

DETERMINATION    OF   LAYOUTS 

The  determination  of  the  best  possible  layout  for  any  proposed  structure 
is  truly  an  economic  problem,  notwithstanding  the  fact  that  many  of  the 
considerations  which  influence  it  may  not  bear  directly  on  the  question  of 
cost.  It  is  one  of  the  most  important  responsibihties  in  the  province  of  the 
bridge  engineer,  and  to  do  the  work  in  the  most  effective  manner  possible 
demands  a  wide  experience,  coupled  with  good  judgment  and  the  ability  to 
foresee  eventuahties  over  a  long  period  of  years.  The  general  idea  that  the 
best  possible  layout  is  the  one  which  makes  the  first  cost  of  structure  -a 
minunum  is  a  fallacy;  for  there  are  many  other  considerations  besides 
economy  in  initial  expenditure  that  are  of  great  importance.  The  follow- 
ing is  a  fairly  complete  list  of  the  various  items  which  should  be  carefulty 
considered  before  settling  finally  upon  the  layout  of  grades,  clearances, 
span-lengths,  character  of  substructure,  and  type  of  superstructure  to 
adopt.  This  is  a  long  list,  but  it  must  be  remembered  that  it  is  intended 
to  cover  all  the  considerations  for  all  cases,  and  that,  probably,  only  a  few 
of  the  items  will  apply  to  any  particular  case. 

List  of  Factors  and  Conditions  Affecting  the  Layouts  of  Bridges 

A.  Government  Requirements.  L  Stream  Conditions. 

B.  Grade  and  Alignment.  J.  Foundation  Considerations. 

C.  Geographical  Conditions.  K.  Navigation  Lifluences. 

D.  Commercial  Influences.  L.  Construction  Facilities. 

E.  Property  Considerations.  M.  Erection  Considerations. 

F.  General  Featvires  of  Structure.  N.  ^Esthetics. 

G.  Future  Enlargement.  O.  Maintenance  and  Repairs. 
H.  Time  Considerations.  P.  Economics. 

While  there  is  an  attempt  at  logic  in  the  arrangement  of  the  preceding 
list  on  the  combined  hues  of  natural  sequence  and  comparative  im])ortance, 
it  is  impossible  to  state  in  advance  for  an}^  particular  case  or  class  of  cases 
which  are  the  items  that  should  receive  the  most  consideration.  Each  item 
will  be  taken  up  and  discussed  in  the  order  adopted  in  the  list. 

Government  Recjiiirements 

In  Cliaplcir  L  of  "l')ridge  Engin(MM-ing"  the  re(|uirenients  of  tlie  United 
States  Government  icgulating  th(>  bridging  of  navigable  streams  are  treated 

116 


DETERMINATION   OF   LAYOUTS  117 

at  length.  Neither  the  Federal  GoverniDent  nor  any  of  the  State  Govern- 
ments, however,  concern  themselves  with  the  bridging  of  streams  that  are 
not  navigable,  unless  it  happen  that  suit  against  the  builder  or  the  pio- 
posed  builder  of  the  bridge  be  instituted  in  either  a  State  or  a  Federal  Court, 
when,  of  course,  the  law  will  be  concerned. 

The  War  Department  nearly  always  confines  its  attention  to  a  few 
salient  features  of  any  proposed  crossing  of  a  navigable  stream,  viz.,  the 
span-lengths,  the  clear  waterway  for  navigation,  the  angle  of  skew  (if  the 
crossing  be  not  square) ,  the  position  of  the  movable  span  or  spans  (if  there 
be  any),  the  clear  headway  above  high  water  for  both  the  movable  and  the 
fixed  spans,  the  character  and  the  dimensions  of  the  draw  protection,  and 
the  amount  of  obstruction  to  the  flow  of  water  caused  by  the  piers — espe- 
cially those  parts  thereof  below  low-water  mark. 

In  spite  of  the  fact  that  the  War  Department  has  certain  rules  for  deter- 
mining the  span-lengths  for  crossing  various  navigable  rivers,  the  said  rules 
are  more  or  less  elastic;  hence  it  will  generally  pay  any  consulting  bridge 
engineer,  or  other  engineer  who  intends  to  bridge  navigable  water,  to  con- 
sult first  with  the  local  engineer  of  the  Government  who  has  charge  of  the 
district  in  which  the  proposed  structure  is  located,  and  later,  if  necessary, 
with  headquarters  at  Washington,  in  order  to  settle  as  to  what  the  exact 
requirements  of  the  Government  will  be.  Often  by  stating  one's  case 
clearly  and  logically  one  can  persuade  the  authorities  to  ease  up  on  some 
regulation  that  appears  to  be  unnecessarily  strenuous  or  severe.  For 
instance,  the  relation  between  the  widths  of  clear  openings  required  for 
swing  spans  and  bascules  or  vertical-lift  spans  is  a  matter  that  has  never 
been  finally  determined  by  the  Department,  each  case  as  it  arises  being 
solved  on  its  own  merits. 

Again,  if  the  limiting  length  of  span  set  by  the  Government  does  not 
exactly  fit  a  crossing,  one  has  to  put  in  a  shorter  span  at  one  end  of  the 
bridge,  or  to  increase  equally  all  the  span-lengths,  or  else  to  obtain  permis- 
sion to  decrease  them  equally.  If  the  decrease  be  small,  it  is  sometimes 
practicable  to  obtain  the  consent  of  the  Department  to  the  adoption  of  the 
shortened  span-length. 

In  the  case  that  the  grade  of  a  bridge  is  so  low  as  to  bring  the  clearance 
line  too  close  to  the  elevation  of  high  water  to  meet  the  Government 
requirements,  it  is  sometimes  possible  to  persuade  the  Department  to  per- 
mit an  encroachment;  but  to  do  so  would  certainly  be  bad  policy,  for  the 
limit  set  by  the  United  States  Engineers  is  adjusted  about  right  to  provide 
safety  from  passing  drift. 

In  respect  to  the  position  of  the  movable  span,  the  broad  statement  can 
be  made  that  its  mid-length  should  coincide  with  the  deepest  part  of  the 
channel,  but  there  are  occasional  exceptions  to  the  rule,  notably  when  the 
channel  is  not  permanent,  or  where  it  can  advantageously  be  shifted  by  a 
little  dyking.  Permission  to  do  such  shifting  and  to  locate  the  movable 
span  accordingly  would  have  to  be  obtained  from  the  War  Department. 


118  ECONOMICS   OF   BRIDGEWORK  Chapter  XV 

The  latter  may  have  something  to  say  about  the  angle  of  skew,  as  the 
United  States  Engineer  Corps  always  advocates  a  square  crossing,  if  it  be 
practicable;  hence  the  bridge  engineer  who  deskes  to  obtain  approval  for  a 
bridge  on  a  skew  of  any  magnitude  must  be  prepared  to  show  good  reason 
for  his  request;  and  even  then  it  may  not  be  granted,  because,  like  the 
author,  the  Govermnent  engineers  look  upon  a  skew  bridge  as  an  abom- 
ination. 

While  the  Department  does  not  pay  much  attention  to  the  character  of 
the  draw  protection,  it  is  likely  to  insist  that  it  be  not  omitted  and  that  its 
dimensions  be  satisfactory. 

Ordinarily,  also,  it  does  not  concern  itself  with  the  dimensions  of  the 
substructure;  but  sometimes,  especially  in  case  of  a  skew  bridge,  objection 
is  raised  to  placing  too  much  rip-rap  around  the  piers  and  thus  obstructing 
the  flow  of  water  in  the  channel. 

Grade  and  Alignment 

In  most  cases  the  grade  and  the  alignment  of  the  railroad  or  travelway 
are  determined  before  the  bridge  engineer  is  called  in,  but  sometimes  it  is 
otherwise;  and  there  arise  occasionally  conditions  which  compel  a  con- 
scientious bridge  specialist  to  insist  upon  a  change  in  either  the  grade  or 
the  alignment — or  in  both. 

The  ideal  way  to  adjust  the  grade  on  a  structure  is  to  carry  it  over 
unbroken  and,  preferably,  level  in  the  case  of  railroad  bridges,  thus  avoiding 
either  a  sag  or  a  hump,  as  either  of  these  objectionable  conditions  involves 
loss  of  power  due  to  the  climbing  of  unnecessary  grades.  Again,  any  great 
sag  causes  traction  stresses  and  a  shock  that  might  better  be  avoided,  if 
practicable.  In  a  highway  bridge  this  is  not  so  important,  and  a  rise 
from  ends  to  centre  of  structure  is  permissible,  especially  as  it  facilitates 
drainage  and  improves  appearance,  notably  in  long-span  suspension- 
bridges. 

The  ideal  alignment  for  a  structure  is  not  only  to  have  it  on  tangent 
throughout  its  entire  length,  but  also  to  continue  the  said  tangent  quite  a 
distance  away  from  the  bridge  at  each  end.  Sharp  curves  constitute  an 
invitation  for  derailment;  and  a  derailment  on  a  bridge,  or  near  the  end  of 
one,  is  liable  to  prove  disastrous.  A  reverse  curve  on  a  structure,  or  on  an 
approach  thereto,  is  not  permissible,  if  it  can  possibly  be  avoided.  Where 
two  curves  in  opposite  directions  come  close  together,  there  should  be  a 
stretch  of  tangent  b(;tween  them;  and  when  this  tangent  is  on  a  bridge,  it 
should  be  made  as  long  as  possible.  Sometimes  it  is  entirely  impracticable 
to  avoid  curvature  on  bridges  and  their  approaches,  as  in  the  case  of  a  rail- 
road following  the  course  of  a  river  that  runs  between  high  banks  and  having 
to  cross  it  from  time  to  time  in  order  to  avoid  heavy  excavations  and  tun- 
neling. In  su(;h  cases  curves  on  the  approaches  are  unavoidable,  and  often 
it  is  necessary  to  put  a  part  of  even  the  whole  of  the  structure  itself  on  curve. 


DETERMINATION   OF   LAYOUTS  119 

Such  a  general  condition  existed  on  the  Hne  of  the  Canadian  Northern 
Pacific  Railway  as  it  followed  up  the  Fraser  and  the  Thompson  rivers, 
crossing  them  nine  times  with  only  one  structure  entirely  on  the  square. 

In  some  skew  crossings,  especially  when  the  obliquity  is  small,  it  is 
permissible  to  square  the  piers  to  the  structure,  thus  saving  considerable 
masomy;  but  this  practice  is  not  always  advisable  because  of  the  damming 
of  the  water  by  the  large  area  of  the  substructure  that  is  opposed  to  the 
current 

The  layout  of  any  bridge  on  a  curve,  or  which  has  its  approaches  on 
curve,  is  greatly  affected  by  the  curvature,  in  that  it  has  a  tendency  to 
shorten  the  span-lengths  in  the  effort  to  avoid  excessive  width  of  superstruc- 
ture and  undue  increase  in  length  of  piers. 

The  determination  of  the  best  grade  to  use  for  the  approaches  to  a 
bridge  is  an  economic  problem  of  major  import.  It  is  of  much  more  con- 
sequence in  railroad  bridges  than  in  highway  structures,  because  of  the  far 
steeper  grades  which  are  permissible  in  the  latter;  for,  of  course,  the  steeper 
the  grade  the  shorter  the  approach  and  the  less  its  cost.  It  is  sometimes 
practicable  to  put  a  grade  on  the  river  spans  of  a  bridge,  leading  up  to  a 
movable  span  or  to  a  single,  high-level  channel-span;  and  this  should 
always  be  done  when  practicable,  notwithstanding  the  fact  that  the  grade 
may  have  to  be  less  than  that  allowable  for  the  approaches,  because  even 
inches  in  elevation  on  the  land  construction  often  count  materially  in 
determining  the  length  and  cost  thereof. 

In  railroad  bridges  the  fixing  of  the  approach  grades  sometimes  involves 
the  economic  solution  of  the  question  of  a  steep  grade  with  pusher  engines 
versus  an  easy  grade  without  them.  In  this  case  it  is  necessary  to  add  to 
the  first  cost  of  the  former,  the  first  cost  of  all  the  pusher  engines  needed, 
plus  the  capitalized  value  of  the  annual  cost  of  their  operation  and  deterio- 
ration, and  compare  the  sum  with  the  first  cost  of  the  latter.  Moreover 
when  figuring  the  annual  cost  of  operation,  it  is  necessary  to  include  therein 
the  annual  expense  due  to  delay  of  trains  caused  by  stopping,  attaching  the 
pushers,  and  regaining  speed. 

Geographical  Conditions 

The  layout  of  a  bridge  is  sometimes  influenced  to  a  certain  extent  by 
its  geographical  location,  because  a  structure  suitable  for  the  heart  of  a  city 
might  not  be  appropriate  in  a  country  district,  and  vice  versa.  Generally 
the  variation  involved  would  be  a  question  of  aesthetics,  or  possibly  one  of 
flooring,  for  sometimes  it  is  necessary  to  cover  over  the  deck  of  a  railroad 
bridge  so  as  to  permit  it  to  take  care  also  of  highway  traffic.  In  mountain- 
ous districts  where  the  transportation  of  large,  heavy  pieces  is  either  very 
expensive  or  altogether  impracticable,  the  layout  would  be  governed  by  this 
condition. 


120  ECONOMICS   OF   BRIDGE  WORK  Chapter  XV 

Commercial  Influences 

The  principal  commercial  consideration  that  will  affect  the  layout  of  a 
bridge  is  the  amount  and  character  of  the  traffic  of  which  it  will  have  to  take 
care.  If  there  is  a  variety  of  traffic,  such  as  steam  railwaj',  electric  railway, 
wagon,  and  pedestrian,  considerable  attention  must  be  paid  to  the  question 
of  how  best  to  take  care  of  all  probable  combinations  of  the  different  kinds. 
Much  money  can  be  saved  for  a  chent  by  a  bridge  engineer  W'ho  knows  how 
to  handle  the  question;  and  much  can  be  wasted  by  one  who  is  not  properly 
posted  on  this  important  subject.  An  indisputable  proof  of  the  correctness 
of  the  latter  statement  is  furnished  by  the  notorious  case  of  a  proposed 
bridge  to  cross  the  Second  Narrows  at  Vancouver,  B.  C.  In  that  layout 
three  railway  tracks  were  adopted  where  two  would  have  served  the  pur- 
pose equally  well,  with  the  result  that  the  estimated  cost  of  the  structure 
was  increased  about  seven  hundred  and  fifty  thousand  dollars,  and  the 
project,  in  consequence,  was  either  killed  or  relegated  for  consummation  to 
the  dim  and  distant  future. 

Property  Considerations 

Property  considerations  sometimes  have  a  far  greater  effect  on  the  lay- 
out of  a  structure  than  is  at  all  legitimate.  For  instance,  in  the  case  of  the 
Northwestern  Elevated  Railroad  of  Chicago,  engineered  by  the  author  in 
the  early  nineties,  certain  high  prices  for  land  caused  the  company  to  lay 
out  such  a  crooked  line  as  to  interfere  materially  with  the  attainment  of  a 
satisfactory  train  velocity.  Refusal  of  property  owners  to  allow  the  con- 
struction of  piers  or  pedestals  on  their  land  will  often  oblige  an  engineer  to 
adopt  an  unduly  long  span,  or  even  an  entirely  different  type  of  construc- 
tion from  the  ordinary.  Again,  the  necessity  for  occupying  a  certain  city 
street  will  sometimes  change  entirely  the  character  and  layout  of  an 
approach  to  a  bridge,  and  it  might  affect  even  the  layout  of  the  bridge  itself. 
The  method  of  crossing  a  railroad  track  at  the  entrance  to  a  bridge  might 
alter  fundamentally  the  type  of  structure,  a  low  bridge  with  an  opening 
span  being  adopted  if  the  crossing  be  at  grade,  and  a  high  bridge  with  fixed 
spans  if  it  be  overhead.  Public  improvements  sometimes  cause  material 
modifications  of  plans  for  proposed  bridges;  and  even  projected  improve- 
ments with  prior  rights  are  liable  to  cause  troublesome  interference.  The 
author  has  lately  encountered  obstructive  opposition  of  this  nature  on 
a  big  bridge  project. 

General  Features  of  Structure 

The  question  of  wh(>ther  tluougli,  deck,  or  half-through  truss  spans  or 
girders  are  adoptt^d  is  one  that  will  radically  affect  the  layout,  but  mainly 
in  tin;  line  of  economics,  because^  d(H;k  structures  in  most  cases  involve  a 
saving  of  expense  in  both  substructure  and  superstructure,  in  that  the 


DETERMINATION    OF    LAYOUTS  121 

piers  are  shorter  than  those  for  through  or  half-through  spans,  and,  gen- 
erally, the  spans  are  narrower,  thus  causing  a  saving  of  metal  in  both  the 
cross-girders  and  the  lateral  bracing.  The  clear  headway  required, 
especially  for  short  spans,  is  likely  to  influence  the  layout  more  or  less. 

The  possibility  of  using  buried  piers  and  protecting  the  feet  of  the 
embanlonents  near  them  by  rip-rap  will  not  only  affect  the  physical 
appearance  of  the  bridge,  but  also  it  will  modify  the  economics  of  the 
crossing. . 

In  case  a  bridge  is  to  cross  a  navigable  stream,  the  layout  of  spans  will 
depend  primarily  upon  whether  a  swing,  bascule,  or  vertical-lift  span  is 
adopted  for  the  opening.  If  a  swing  is  employed,  it  will  generally  require 
an  expensive  draw  protection,  while  for  a  bascule  or  a  vertical  lift  some 
comparatively  inexpensive  dolphins,  either  with  or  without  cheap  fender- 
walls  of  sheathed  piles,  will  suffice. 

The  possibility  of  building  an  arch,  a  cantilever,  or  a  suspension  bridge 
instead  of  a  simple-span  structure  would  affect  the  layout  in  many  ways — 
physically,  aesthetically,  and  economically. 

Again,  the  material  adopted  for  construction — whether  masonry,  con- 
crete, steel,  or  timber — will  have  a  similar  influence. 

The  matter  of  shore  protection  is  not  likely  to  affect  directly  the  layout 
for  a  bridge,  although  its  use  certainly  does  increase  the  total  cost;  but 
it  might  be  the  reason  for  shifting  the  crossing  to  a  location  where  the 
bank  is  better  protected  by  nature  against  scour. 

Finally,  the  layout  is  affected  by  the  character  of  the  approaches;  for 
they  may  be  of  earth  embankment,  timber  or  pile  trestle,  steel  viaduct,  or 
reinforced-concrete  girders  or  arches. 

Future  Enlargement 

The  possibility  of  future  enlargement  of  structure  ought  to  receive 
consideration;  and  if  it  be  decided  that  it  is  at  all  probable,  a  study  of  the 
layout  should  be  made  so  as  to  determine  how  best  to  accomplish  such 
enlargement  when  the  time  comes  for  so  doing.  The  points  to  consider 
are  whether  it  will  be  best  to  build  an  entirely  separate  new  bridge  close 
alongside,  or  to  put  a  double-track  superstructure  on  the  old,  single-track 
piers  by  enlarging  them  or  expanding  their  tops,  or,  at  the  outset,  to  put 
in  large  piers  and  build  thQ  superstructure  in  such  a  manner  that  the 
trusses  can  be  doubled  in  the  future. 

Again,  it  would  frequently  be  good  engineering  to  provide  at  first 
only  the  floor  systems  necessary  to  suffice  for  traffic  requirements  at  the 
outset,  but  to  design  the  trusses  and  substructure  so  that  additional 
roadways  and  tracks  can  be  added  in  the  future  when  needed. 

Time  Considerations 

The  time  allowed  for  completing  the  substructure  or  the  superstructure 
or  the  whole  bridge  may  affect  the  layout,  for  it  is  understandable  that  a 


122  ECONOMICS   OF   BRIDGEWORK  Chapter  XV 

certain  type  of  structure  could  be  built  in  a  certain  limited  time  while 
another  type  of  structure  could  not.  Again,  the  length  or  shortness  of 
the  working  season  that  is  entirely  free  from  danger  of  washout  of  false- 
work could  be  a  sufficient  reason  for  changing  materially  the  layout — for 
instance,  by  necessitating  pin-connected  spans  instead  of  riveted  ones,  or 
steel  truss-spans  instead  of  concrete-arch  ones,  or  semi-cantilevering  of 
certain  spans  instead  of  falsework  erection  throughout. 

Stream  Conditions 

The  various  influences  of  the  stream  that  is  to  be  crossed  are  more 
potent  than  most  other  factors  in  affecting  the  layout.  The  high-water- 
and  the  low-water-elevations  are  important  features  in  the  designing 
of  the  piers;  the  amount  and  character  of  the  drift  determine  the  minimum 
vertical  distance  between  high  water  and  the  bottom  of  the  superstructure, 
and,  therefore,  aid  in  settling  the  pier  height;  and  the  amount  and  con- 
sistency of  the  passing  ice  constitute  an  important  factor  in  the  design 
of  the  piers,  especially  in  respect  to  their  length  and  the  character  of 
their  end  finish;  and  any  increasing  of  the  cost  of  the  piers  tends,  for 
economic  reasons,  to  lengthen  the  spans. 

The  clear  waterway  required  to  pass  the  probable  maximum  flood  will 
often  settle  the  total  length  of  structure;  and  it  may  result  in  raising  the 
high-water  mark  that  was  determined  in  some  other  manner.  The  profile 
of  the  river-bed  and  the  probable  scour  of  the  materials  of  which  it  is 
composed  are  likely  to  affect  the  layout,  especially  if  the  piers  require 
expensive  protection  of  mattress  work  and  rip-rap  to  check  the  said  scour. 
The  frequency  and  extent  of  the  floods  will  influence  the  cost  of  building 
the  piers — hence  also  the  determination  of  the  layout — as  will  also  the 
questions  of  rise  and  fall  of  tides,  velocities  of  the  passing  water,  reversal 
of  current,  and  the  existence  or  possible  future  building  of  levees. 

A  most  important  factor  is  the  possibility  of  the  permanent  shifting 
of  the  channel  from  one  side  of  the  river  to  the  other.  If  this  possibilitj'' 
exist,  one  of  three  things  must  be  done,  viz. :  first,  two  movable  spans  must 
be  provided;  second,  some  effective  method  of  retaining  the  channel  in 
one  position  must  be  arranged  for;  or,  third,  the  design  must  be  so  made 
that  any  fixed  span  of  the  structure  may  at  any  time  be  converted  into  a 
vertical-lift  span. 

Foundation  Considerations 

Important  also  in  the  determination  of  layout  are  the  character  and 
the  depth  of  the  substructure  foimdation.  The  deeper  the  piers  have  to 
go  the  longer  will  be  the  economic  lengths  of  the  spans.  Again,  the  more 
difficult  it  is  to  penetrate  the  materials  overlying  the  bed-rock  or  final 
foundation,  the  greater  the  cost  of  the  piers,  and  the  longer  the  economic 
spans.     The  ultimate  depths  to  foundation  and  the  materials  to  be  penc- 


DETERMINATION   OF   LAYOUTS  123 

trated  determine  what  process  of  sinking  to  adopt;   and  as  the  cost  of  the 
substructure  depends  upon  the  said  process,  so  also  will  the  layout. 

Navigation  Influences 

The  influences  of  navigation  that  are  likely  to  prevail  during  the  time 
of  the  contractor's  operations  may  be  of  such  moment  as  to  affect  more  or 
less  the  design  and  the  layout  of  the  structure;  although  this  is  not  very 
likely.  Again,  the  possibility  in  the  future  of  greatly  augmented  river- 
traffic  may  influence  the  type  of  movable  span  adopted. 

Construction  Facilities 

The  availability  or  otherwise  at  the  bridge  site  of  sand,  gravel,  concrete- 
stone,  a  machine  shop  for  repairs,  and  a  reliable  source  of  supplies  for  the 
work  and  workmen,  the  accessibility  or  the  contrary  of  the  site  from  the 
nearest  railroad  depot  or  siding,  the  length  and  difficulty  of  wagon-haul 
or  other  means  of  transportation  of  materials  and  supplies,  the  facilities 
for  securing  and  retaining  labor,  and  the  availabihty  of  supplies  of  timber 
and  pihng  all  affect  greatly  the  cost  of  the  substructure  and  to  possibly  a 
somewhat  less  degree  that  of  the  superstructure — hence  also  the  layout 
of  spans  and  piers. 

Erection  Considerations 

The  difficulties  that  may  be  anticipated  for  erection,  and  the  method 
thereof  finally  adopted,  whether  by  falsework,  cantilevering,  semi-canti- 
levering,  or  flotation,  are  important  factors  affecting  the  layout  of  the 
structure,  as  are  also  the  questions  of  the  maintenance  of  traffic  and  the 
replacement  of  an  existing  bridge. 

J^sthetics 

Too  often  the  question  of  aesthetics  is  totally  ignored;  but  when  it  is 
given  proper  consideration,  it  may  cause  modifications  in  span  lengths, 
truss  dimensions,  and  shapes  of  piers.  How  much  extra  money  it  is 
legitimate  for  a  bridge  engineer  to  spend  for  the  purpose  of  beautifying 
a  structure  is  a  mooted  point.  It  depends  greatly  upon  the  designer's 
appreciation  of  the  beautiful  in  nature  and  in  art,  as  well  as  upon  the 
elasticity  of  the  client's  purse  and  the  extent  of  the  influence  upon  him 
exerted  by  his  consulting  engineer,  also  upon  the  location  and  surroundings. 
Generally  speaking,  the  best  layout  for  aU  the  other  ruHng  causes  is  the 
best  also  for  aesthetic  reasons;  but  there  are  cases  when  a  little  extra 
expenditure  of  money,  time,  and  brains  will  secure  great  improvement  in 
appearance;  and  in  such  cases  the  beautifying  of  the  construction  should, 
if  possible,  be  accomplished. 


124  ECONOMICS   OF   BRIDGEWOEK  Chapter  XV 

Maixtexaxce  and  Repairs 

The  cost  of  maintenance  and  repairs  as  well  as  that  of  operation  may 
sometimes  be  a  vital  consideration  affecting  the  layout  of  a  structure. 
For  instance,  when  the  Jefferson  City  highway  bridge  over  the  Missouri 
River  was  about  to  be  built,  the  bridge  company,  in  spite  of  the  author's 
forcible  remonstrance,  let  the  contract  for  the  structure  on  the  basis  of  a 
high  bridge  with  a  long  and  expensive  timber  trestle  approach.  Later 
they  were  convinced  that  the  annual  expense  of  maintaining  the  said 
trestle  would  be  so  great  as  to  consume  more  than  the  total  net  income 
from  traffic  receipts;  hence  they  had  to  change  to  a  low  bridge  design. 

Theoretical  Economics 

From  time  to  time  an  engineer  encounters  a  bridge  problem  in  which 
the  controlling  factor  in  the  layout  determination  is  really  that  of  economics, 
and  then  he  is  happy;  for,  comparatively  speaking,  the  case  is  a  smiple  one. 
A  case  of  this  kind  occurred  in  the  author's  Canadian  Northern  Pacific 
Railway  bridge  across  the  North  Thompson  River,  near  Kamloops,  B.  C. 
The  structure  consists  of  a  number  of  deck,  plate-girder  spans,  one  of 
which  is  lifted  so  as  to  permit  of  the  passage  of  small  river  steamers  at 
certain  high  stages  of  water. 

The  requirements  of  aesthetics  often  conflict  with  those  of  economics; 
for  it  would  not  look  well  to  let  the  span  lengths  change  backward  and 
forward,  perhaps,  to  suit  the  vagaries  of  an  unusual  bed-rock  profile; 
hence  it  is  best  in  many  cases  to  compute  the  economic  span  length  for 
average  conditions  of  pier  cost  and  to  use  one  length  instead  of  several. 
It  will  generally  be  found  that  such  an  arrangement  does  not  involve  any 
extra  expenditure  worth  mentioning  when  the  cost  of  structure  for  that 
layout  is  compared  with  that  for  the  truly  economic  one.  The  question 
of  economics,  however,  cannot  be  finally  settled  by  adopting  simply  that 
structure  for  which  the  initial  cost  is  a  minimum;  because,  as  pointed  out 
previously,  the  truly  economic  bridge  is  the  one  for  which  the  sum  of  the 
first  cost  and  the  capitalized  annual  cost  of  operation,  maintenance,  and 
repairs  is  a  minimum. 

As  a  conclusion  to  the  general  subject  under  discussion,  in  order  not 
to  discourage  young  (engineers,  it  might  be  well  t(i  state  that  any  designer 
who,  when  deterniiiiing  the  layout  for  any  largo  and  impoi-fant  ])i'idge, 
can  and  does  giv(^  full  and  (lu(>  consideration  to  all  the  fai'tors  treated  in 
this  chapter,  is  truly  worthy  to  be  ternuxl  an  ex])ert  bridge  engin(H>i'. 


CHAPTER  XVI 

ECONOMICS    OF   LOADS   AND    UNIT    STRESSES 

The  determination  of  the  live  loading  for  any  proposed  structure  is  an 
economic  problem  of  prime  importance;  and  it  often  involves  the  employ- 
ment of  engineering  talent  of  the  highest  order.  As  a  rule,  that  loading 
should  be  made  large  enough  to  take  care  of  the  greatest  moving  loads 
that  may  reasonably  be  expected  to  come  often  upon  the  structure  during 
its  lifetime;  and  as  the  latter  for  a  well-designed,  modern  bridge  is  of 
indefinitely  great  length,  the  problem  is  by  no  means  an  easy  one  to  solve. 
It  must  be  recognized  that  the  occasional  application  of  a  load  exceeding 
by  25  per  cent,  or  even  more,  the  one  used  in  making  the  design,  will  do 
no  harm  to  the  structure,  but  that  when  the  excess  reaches  50  per  cent 
and  is  applied  often  the  condition  begins  to  become  serious. 

While  it  is  right  and  proper  for  an  engineer  to  act  with  precaution  by 
assuming  the  live  load  great  enough  to  meet  all  likely  contingencies,  it 
would  be  uneconomic  to  attempt  to  provide  for  improbable  or  impossible 
loadings.  Again,  while  it  is  feasible  to  subject  a  short  span  to  a  very 
heavy  loading,  it  is  not  so  in  the  case  of  a  long  one;  and  the  longer  the 
span  the  smaller  is  the  chance  of  its  ever  having  to  carry  an  abnormally 
great  live  load.  This  remark  applies  more  forcibly  to  highway  bridges 
than  to  steam-railway  structures;  although  it  undoubtedly  holds  good  to  a 
certain  extent  for  the  latter,  because  it  is  very  seldom  that  long  trains 
are  composed  entirely  of  the  heaviest  kinds  of  loaded  cars.  About  the 
only  exception  to  this  rule  is  in  the  case  of  a  structure  on  a  railroad  carrying 
long  trains  of  fully-loaded  ore-cars  or  coal-cars. 

There  is  one  point  in  connection  with  highway  live  loadings  that  is 
of  importance,  viz.,  that  all  new  highway  bridges  should  be  proportioned  to 
carry  heavy  trucks.  The  concentrated  loads  caused  by  these  are  so  great 
that  the  old-fashioned  wooden-joist  floors  will  not  be  able  to  carry  them. 
There  is  no  telling  how  far  from  home  these  exceedingly  heavy  auto- 
trucks will  travel,  so  that  no  out-of-the-way  highway  bridge  will  be  safe 
from  their  invasion.  Again,  it  must  be  remembered  that  auto-truck  loads 
are  rapidly  on  the  increase;  hence  one  should  be  hberal  in  his  assumptions 
for  this  feature  of  the  live  loading. 

In  respect  to  live  loading  in  general,  it  seems  almost  unnecessary  to 
mention  that  the  amount  thereof  decreases  slowly  with  the  span-length. 
In  steam-railway  structures  this  is  primarily  because  the  effect  on  the  total 
span-length  of  the  greater  weight  per  foot  of  the  coupled  standard  locomo- 

125 


126  ECONOMICS   OF   BRIDGEWORK  Cilipter  XVI 

tives,  as  compared  with  that  assiuned  for  the  loaded  cars,  diminishes  as  the 
span-length  increases;  but  in  highway  bridges  the  lessening  is  due  to  an 
application  of  the  theory  of  probabilities.  For  the  electric-railway  loading 
the  diminution  in  the  equivalent  hve  load  per  lineal  foot  exists  only  when 
the  length  of  span  is  greater  than  the  assumed  total  length  of  train,  and 
the  greater  the  difference  in  length  the  greater  the  said  diminution  of  load- 
ing per  lineal  foot  of  span.  On  pages  110  to  116,  inclusive,  of  "Bridge 
Engineering"  are  given  curves  of  equivalent  uniform  loads  for  trains  of 
two,  three,  four,  five,  and  six  electric-railway  cars  and  for  aU  the  classes  of 
loading  from  15  to  40.  These  are  carried  out  to  a  length  of  only  600  feet; 
and  in  case  of  longer  spans  it  would  become  necessary  to  lengthen  them 
either  accurately  by  computation  or  approximately  by  visual  extension. 

For  ordinary  railroad  bridges  the  determination  of  the  proper  hve  load 
to  adopt  is  generally  a  simple  affair,  because  the  company  is  likely  to  have 
a  standard  of  its  own;  but  sometimes  it  may  be  advisable  to  depart  from 
this,  in  order  to  provide  for  some  unusual  condition  or  complication. 
For  highway  bridges,  though,  it  is  a  different  matter,  because  the  amount 
and  character  of  the  traffic  will  depend  greatly  on  local  conditions;  and, 
consequently,  the  size  of  the  loading  is  a  question  of  judgment.  In 
exercising  it,  one  should  look  to  the  possibility  of  a  material  increase  in 
the  weights  to  be  transported;   and  should  be  governed  accordingly. 

The  standard  steam-railway  loadings  given  in  Chapter  VI  of  "Bridge 
Engineering"  are  still  sufficient  for  maximum  requirements,  and  it  is  not 
likely  that  the  greatest  (Class  70)  will  ever  be  materially  exceeded,  unless 
some  fundamental  improvement  be  made  in  the  character  of  railway 
roadbeds.  The  distribution  of  weight  on  the  axles  of  the  locomotives  is 
gradually  being  changed,  but  the  weight  thereof  per  lineal  foot  of  track 
does  not  appear  to  be  augmenting  to  any  great  extent. 

The  heaviest  live  loads  for  electric  railways  given  in  the  aforesaid 
chapter  have  not  yet  been  reached,  except  in  the  case  of  electrified  steam- 
railroads;  and  these  are  not  treated  as  real  electric  railways,  as  far  as 
bridge  loadings  are  concerned.  Ordinarily,  Class  25  is  heavy  enough  for 
the  street-railway  live-loads  on  highway  bridges;  but  sometimes  it  is 
advisable  to  proportion  for  Class  30,  in  order  to  provide  for  future  heavy 
suburban  cars. 

Classes  A,  B,  and  C  for  highway  loadings  are  sufficiently  heavy,  even 
if  it  be  possible  to  crowd  vehicles  and  pedestrians  so  close  together  as  to 
cause  the  actual  loadings  to  exceed  them;  because,  when  much  crowding 
occurs,  the  speed  of  travel  is  materially  reduced,  and  then  the  effect 
of  impact  may  practically  be  ignored.  Class  A  loading  is  so  great  that, 
for  comparatively  long  spans  and  wide  decks,  it  may  be  used  to  cover  the 
average  loading  over  the  full  width  of  deck  from  electric-cars,  vehicles, 
and  pedestrians — and  this  applies  in  nearly  all  cases  to  suspension  bridges. 
But  in  that  type  of  bi-idge  it  nmst  be  remembered  that  for  the  stiffening 
trusses  the  equivalent  uniform  live  load  per  lineal  foot  of  structure  must 


ECONOMICS    OF    LOADS    AND    UNIT   STRESSES  127 

be  taken  for  about  four-tenths  of  the  span-length  and  not  for  the  full 
length,  as  is  the  case  for  shnple  spans. 

In  cantilever  bridges  judgment  must  be  used  in  determining  the 
lengths  for  equivalent  uniform  loads  for  the  different  portions  of  structure. 
For  instance,  in  Type-A  cantilever,  shown  in  Fig.  12a,  for  the  suspended 
span  its  total  length  is  to  be  used;  for  the  cantilever  arms  the  sum  of  the 
length  of  the  suspended  span  and  that  of  the  portion  of  the  cantilever 
arm  that  is  loaded  for  maximum  stress  on  the  member  considered;  and 
for  the  anchor  arms  the  total  length  of  the  loaded  portion  of  one  such  arm 
for  direct  loading  and  that  of  one  cantilever  arm  plus  suspended  span  for 
reverse  loading.  A  skilful  bridge  designer  can  often  legitimately  economize 
in  his  work  by  making  a  careful  study  of  the  live-load  question  and  cut- 
ting down  the  loading  as  hereinbefore  indicated. 

Similarly  a  study  of  the  question  of  impact  allowance  and  the  utilization 
of  the  very  latest  information  thereon  will  result  in  a  certain  amount  of 
economy.  For  instance,  since  "Bridge  Engineering"  was  written,  the 
author  has  found  it  advisable  to  modify  the  impact  allowances  recom- 
mended in  Chapter  VII  thereof  in  the  following  particulars: 

First.  For  electric-railway  loads  use  the  same  impact  as  for  highway 
loads.  This  modification  is  based  upon  some  late  experiments  by  Prof. 
Turneaure. 

Second.  When  a  reinforced-concrete  base  is  used  for  the  pavement  of 
a  highway  bridge  with  similar  slabs  for  the  footwalks,  the  impacts  given 
may  be  reduced  twenty-five  (25)  per  cent. 

Third.  For  reinforced-concrete  arches  and  girders,  without  earth 
filling,  the  impacts  may  be  reduced  fifty  (50)  per  cent. 

Fourth.  For  earth-filled,  concrete  arches,  they  may  be  reduced  seventy- 
five  (75)  per  cent. 

The  determination  of  the  width  of  deck  that  it  is  best  to  employ  is  an 
economic  question  of  salient  importance.  A  narrow  roadway  tends  to 
induce  slow  travel,  owing  to  the  necessity  for  reducing  the  speed  of  automo- 
biles in  narrow  places  so  as  to  avoid  collision.  For  two  lines  of  travel  at 
high  speed  a  width  of  twenty-two  feet  is  advisable,  although  one  of  twenty 
feet  is  often  considered  sufficient  because  it  is  practicable  to  pass  most 
auto-vehicles  on  a  width  that  is  two  or  three  feet  less.  There  are  many 
bridges  in  country  districts  that  are  only  eighteen  feet  wide  and  some  as 
narrow  as  sixteen  feet ;  but  these  do  not  meet  with  the  approval  of  automo- 
bile drivers,  because  a  load  of  hay  will  almost  block  the  structure — besides, 
when  one  is  driving  at  high  speed,  he  does  not  like  to  be  compelled  to  slow 
down  when  he  is  approaching  a  bridge  upon  which  there  is  another  vehicle. 

A  thirty  or  thirty-two-foot  width  of  main  roadway  is  better  than  one 
of  twenty  or  twenty-two  feet,  in  that  it  will  permit  a  fast  vehicle  to  turn 
out  and  pass  a  slowly-moving  one;  but  there  is  always  the  danger  of  run- 
ning into  an  automobile  of  the  other  Hne  that  is  trying  to  accomplish  the 
same  purpose.     A  roadway  of  forty  or,  preferably,  forty-two  or  even  forty- 


128  ECONOMICS   OF   BRIDGEWORK  Chapter  XVI 

four  feet  in  the  clear  between  curbs  will  take  care  nicely  of  four  lines  of 
automobiles,  and  the  middle  twenty  feet  thereof  may  carry  a  double  track 
for  an  electric  railway. 

From  the  viewpoints  of  both  economy  and  pubHc  convenience  it  is  better 
to  pass  at  once  from  a  two-line-travel  deck  to  a  four-line-travel  deck, 
because  a  width  great  enough  for  only  three  hues  is  unsatisfactory  in  that, 
as  before  indicated,  it  offers  to  reckless  drivers  a  fine  opportunity  for  head- 
on  colhsion — and,  again,  it  is  not  as  suitable  for  high  speed  as  a  wider  struc- 
ture. It  is  true  that  in  the  case  of  a  total  break-down  it  has  a  decided 
advantage  over  the  two-line-travel  deck,  permitting  vehicles  to  pass 
around  the  obstruction,  but  that  is  not  sufficient  reason  to  warrant  its 
adoption. 

Footwalks  are  often  made  much  wider  than  necessary,  but  sometimes 
too  narrow.  The  minunum  width  should  be  five  (5)  feet,  which  will  just 
permit  two  people  to  wallc  abreast  and  to  carry  umbrellas.  Any  smaller 
width  would  be  uncomfortable,  and  one  a  foot  wider  would  be  better.  A 
width  of  eight  (8)  feet  is  generally  sufficient  for  all  requirements,  but  some- 
times ten  (10)  or  even  twelve  (12)  feet  are  called  for.  If  travel  in  both 
directions  is  permittted  on  the  same  footwalk,  it  should  not  be  made  less 
than  seven  (7)  feet  wide,  and  preferably  nine  (9)  or  ten  (10),  but  it  is  seldom 
good  poUcy  to  allow  such  traffic,  because  the  pedestrian  travel  will  be  faster 
if  it  is  always  kept  to  the  right-hand  side  of  the  structure. 

If  a  bridge  is  very  long,  it  is  not  hkely  that  there  will  be  much  pedestrian 
travel  over  it,  unless  there  be  some  special  inducement  such  as  beautiful 
scenery  or  cool  breezes  in  hot  weather,  consequently  the  omission  of  side- 
walks, either  entirely  or  temporarily,  becomes  an  economic  question  of  some 
importance.  Sometimes,  however,  the  obtaining  of  a  charter  for  building 
the  bridge  is  conditioned  upon  putting  on  sidewalks;  and  in  that  case  the 
only  economy  practicable  would  be  to  obtain  from  the  authorities  per- 
mission to  provide  for  their  future  addition  and  to  omit  them  temporarily 
until  the  development  of  traffic  indicates  their  necessity.  In  very  long 
bridges  it  is  economical  to  reduce  the  sidewalk  width  to  the  absolute  mini- 
mum of  five  (5)  feet,  owing  to  the  small  number  of  people  that  are  likely  to 
pass  over  the  structure  on  foot. 

When  a  steam-railway  bridge  has  to  carry  electric-railway  cars  as  well, 
it  is  often  economic  to  adopt  the  expedient  of  gauntleted  tracks,  i.e.,  sepa- 
rate lines  of  rails  for  the  electric  railway  lying  quite  close  to  the  steam- 
railway  rails  and  with  no  connection  thereto,  switches  being  omitted  and 
the  steam-railway  rails  being  cut  so  as  to  permit  the  wheels  of  the  elec- 
tric-railway cars  to  cross  them  on  a  frog.  This  expedient  obviates  the 
necessity  for  increasing  the  railway  live  loads  in  order  to  provide  for  the 
electric-railway  traffic. 

The  cjuestion  of  what  arrangement  of  decks  to  adopt  for  the  acconmio- 
dation  of  several  kinds  of  traffic  is  an  economic  problem  that  sometimes 
arises  in  a  bridge  engineer's  practice.     It  has  lately  come  up  in  the  author's 


ECONOMICS   OF   LOADS   AND    UNIT   STRESSES  129 

in  a  case  where  a  double-track,  steam-railway  bridge  had  to  carry  in  addi- 
tion a  double-track  electric-railway,  wagon-ways,  and  footwalks.  The 
choice  lay  between  a  double-deck  structure  with  the  steam  railways  below, 
a  combined  double-track  electric-railway  and  wagon-way  above  between 
trusses,  and  footwalks  outside  of  the  wagon-way;  and  a  single-deck  struc- 
ture with  the  double-track  steam-railway  between  trusses  as  before,  a 
combined  single-track  electric-railway  and  wagon-way  on  cantilever  brack- 
ets outside  of  each  truss,  and  a  footwalk  outside  of  each  wagon-way.  For 
reasons  unnecessary  to  state,  the  gauntleted  tracks  between  trusses  for  the 
electric  railway  were  barred.  The  comparison  was  hardly  a  fair  one, 
because  the  single-deck  layout  provided  facilities  superior  to  those  afforded 
by  the  other  layout  in  relation  to  rapid  transit, — there  being  two  roadways 
of  twenty-two  feet  each  instead  of  one  roadway  of  thirty  feet — besides 
avoiding  a  climb  of  some  twenty-five  feet.  Wliile  the  cost  of  the  main 
spans  was  greater  for  the  single-deck  structure  than  for  the  double-deck 
one,  on  the  other  hand  there  was  a  saving  in  the  lengths  and  costs. of  the 
approaches.  It  is  impracticable  to  make  any  general  statement  of  com- 
parative costs  or  advantages  of  these  two  types;  and  each  case  as  it  arises, 
will  have  to  be  worked  out  by  itself  as  a  special  economic  problem.  More- 
over, one  layout  or  the  other,  irrespective  of  cost,  will  be  preferable  from 
the  point  of  view  of  service  or  accommodation,  hence  this  feature  will  have 
to  be  given  serious  consideration. 

As  a  rule,  bridges  for  carrying  both  railway  and  highway  traffic  are 
located  in  or  near  large  cities,  although  an  occasional  structure  of  this  kind 
is  found  in  country  districts.  The  principal  advantage  of  this  type  of 
bridge  is  the  saving  in  first  cost,  and  its  principal  disadvantage  is  a  reluc- 
tance to  cross  over  it  on  the  part  of  timid  drivers,  whose  horses  may  be 
frightened  by  the  trains.  The  saving  in  first  cost  of  a  combined  railway 
and  highway  bridge,  as  compared  with  two  separate  bridges  for  railway  and 
highway  traffic,  is  considerable,  because  the  piers  for  the  combined  bridge 
are  but  little,  if  any,  more  expensive  than  those  for  the  railway  bridge,  and 
because  the  extra  metal  for  the  super-structure  of  the  former  in  comparison 
with  that  of  the  latter  is  very  much  less  in  weight  than  the  metal  required 
for  a  separate  highway  bridge.  The  prejudice  against  combined  bridges 
on  account  of  danger  is  almost  wholly  unfounded,  for  horses  soon  become 
accustomed  to  railway  trains,  and,  when  screens  are  employed  to  hide  the 
latter,  but  little  trouble  is  experienced  on  account  of  frightened  animals. 
These  screens  may  be  made  either  slatted  or  solid,  the  former  offering  less 
resistance  to  the  wind,  and  the  latter  being  the  cheaper.  Moreover,  auto- 
mobiles have  almost  entirely  displaced  horses  in  highway  traffic. 

The  advent  of  the  electric  railway  has  somewhat  complicated  the  ques- 
tion of  designing  combined  bridges,  for  now  it  is  often  necessary  to  accom- 
modate all  kinds  of  traffic  on  the  same  structure. 

Combined  bridges  may  be  divided  into  the  following  classes : 

1.  Structures  having  a  single  deck  for  all  kinds  of  traffic,  the  railway 


130  ECONOMICS   OF  BRIDGEWOEK  Chapter  XVI 

occupying  the  center  of  the  bridge,  and  the  electric  railway  lying  close  to 
one  truss. 

2.  Structures  having  a  single-track  railway  at  the  middle,  a  narrow  foot- 
walk  on  each  side  thereof  inside  of  the  trusses,  and  cantilever  brackets  out- 
side of  the  latter  to  carry  roadways  and  electric  hues.  This  arrangement 
may  be  varied  by  running  the  electric  cars  over  the  main  railway  track,  thus 
leaving  the  wings  free  for  vehicular  traffic. 

3.  Structures  having  a  double-track  railway  inside  of  the  trusses,  with 
long  cantilever  brackets  outside  carrying  wagons  and  electric  lines  next  to 
the  trusses  and  pedestrians  outside.  This  arrangement  may  be  varied,  as 
in  Case  2,  by  carrying  the  electric  trains  on  either  one  or  both  of  the  main 
railway  tracks. 

4.  Structures  having  a  double-track  railway  inside  of  the  trusses,  with 
short,  cantilever  brackets  for  wagon  and  electric-railway  traffic  outside, 
and  either  a  single  passageway  overhead  at  the  middle  for  pedestrians,  or 
two  passageways  therefor  on  overhead  brackets  outside  of  the  trusses. 
As  before,  this  arrangement  may  be  modified  by  running  the  electric  trains 
over  the  main  railway  tracks. 

5.  Double-deck,  single-track  structures  carrying  a  railway  train  on  one 
deck  and  vehicles  and  pedestrians  on  the  other.  If  electric  cars  also  are 
carried,  they  should  generally  use  the  railway  track  on  account  of  the  nar- 
rowness of  the  bridge;  but  by  putting  the  railway  below  and  using  canti- 
lever brackets  above,  the  electric  cars  may  share  the  wagon-way  and  run 
over  either  one  or  two  tracks.  When  the  electric  cars  and  the  vehicles 
occupy  jointly  the  upper  deck,  it  is  generally  best  to  carry  the  pedestrians 
by  cantilever  brackets  on  the  lower  deck,  as  the  structure  might  be  too 
narrow  to  warrant  caring  for  them  above  by  footwalks  outside  of  the  joint 
wagon  and  electric  car  roadway  and  because  permitting  them  to  use  the 
said  joint  roadway  would  be  too  hazardous. 

6.  Double-deck,  double-track  structures  carrying  railway  trains  on 
one  deck  and  vehicles,  electric  trains,  and  pedestrians  on  the  other,  or  with 
the  electric  trains  using  the  steam  railway  tracks.  The  vehicles  and  electric 
trains  may  either  occupy  the  same  roadwaj^,  or  the  former  may  be  carried 
on  cantilever  brackets,  leaving  the  middle  portion  of  the  deck  for  the  latter. 
In  such  a  bridge  the  footwalks  should  be  on  cantilever  brackets,  either  above 
or  below,  outside  of  the   other  roadways. 

In  double-deck  structures  where  the  steam  railroad  is  below,  it  is  neces- 
sary to  use  every  precaution  for  keeping  the  locomotive  fumes  away  from 
the  upper  deck,  as  smoke  rising  through  the  floor  frightens  horses  even 
more  than  does  the  train  itself.  Moreover,  smoke  is  exceedingly  disagree- 
able to  everybody  passing  over  the  structure.  Again,  the  question  of 
protecting  the  highway  floor  from  being  set  on  fire  by  sparks  from  locomo- 
tives must  be  satisfactorily  solved  in  this  (•om])inati()n. 

Class  No.  1  is  the  cheapest  possible  kind  of  combined  bi-idge,  and  at 
the  same  time  the  most  unsatisfactory,  for  a\  hen  a  railroad  train  is  about 


ECONOMICS   OF   LOADS   AND    UNIT   STRESSES  131 

to  pass  over  the  structure  all  vehicular  and  electric-railway  travel  must  be 
kept  off,  and  because  pedestrians  must  look  out  sharply  for  their  safety 
when  on  the  deck  with  a  railway  train  crossing.  Their  danger  is  really 
greater,  though,  when  an  electric  train  is  passing  a  team  or  teams.  The 
least  allowable  clear  width  of  bridge  for  this  class  of  structure  is  twenty 
feet,  the  electric  cars  running  on  a  third  rail  and  on  one  of  the  rails  of  the 
main  railway. 

Class  No.  2  is  a  very  satisfactory  type  of  structure.  The  author  has 
designed  and  built  several  bridges  of  this  kind,  the  largest  of  which  is  the 
Combination  Bridge  Company's  bridge  over  the  Missouri  River  at  Sioux 
City,  Iowa.  It  consists  of  two  draw-spans  of  470  feet  each  and  two  fixed 
spans  of  500  feet  each,  besides  the  deck  approach  spans,  the  distance 
between  central  planes  of  trusses  being  twenty-five  (25)  feet. 

Class  No.  3  is  also  a  satisfactory  type  of  structure.  The  author  once 
built  a  large  bridge  of  this  type,  viz.,  the  one  across  the  Missouri  River  at 
East  Omaha,  Nebraska.  This  class  of  structure  involves  very  heavy  metal- 
work;  but  it  is  not  uneconomical. 

Class  No.  4  is  an  unusual  type,  and  is  not  likely  to  be  called  for  very 
often,  although  the  author  has  had  occasion  to  figure  on  bridges  of  this  kind. 

Class  No.  5  gives  a  satisfactory  distribution  of  traffic,  as  was  proved  by 
the  author's  bridge  over  the  Fraser  River  at  New  Westminster,  British 
Columbia.  In  this  the  steam  railway  and  the  electric  cars  occupy  a  single 
track  on  the  lower  deck;  and  vehicles  and  pedestrians  use  in  common  a 
sixteen  (16) -foot  clear  roadway  on  the  upper  deck. 

Early  in  1908  in  preparing  a  design  for  a  combined  bridge  to  carry  a  rail- 
way, a  street-railway,  wagons,  and  pedestrians  over  the  Second  Narrows  of 
Burrard  Inlet  at  Vancouver,  British  Columbia,  the  author  evolved  a  rather 
novel  method  of  dividing  the  traffic.  The  bridge  was  to  be  built  at  first  to 
carry  only  the  railway  and  the  street-railway,  but  provision  was  to  be  made 
to  take  care  of  wagon  and  pedestrian  traffic  in  the  future.  The  distance 
between  central  planes  of  trusses  being  restricted  from  motives  of  economy 
to  the  least  consistent  with  the  Dominion  Government's  requirements  for 
clear  roadway — in  this  case  nineteen  (19)  feet — it  would  have  been  improper 
construction  to  put  twelve  (12)  foot  roadways  outside  of  the  trusses  and 
six  (6)  foot  sidewalks  outside  of  these;'  for  such  an  arrangement  would  make 
each  cantilevered  portion  of  the  deck  wider  than  the  distance  between 
trusses,  while  good  practice  does  not  permit  it  to  exceed  two-thirds  thereof. 
As  the  clearance  above  high  water  was  ample  on  account  of  there  being  an 
overhead  crossing  of  the  Canadian  Pacific  Railway  tracks  at  the  south  end 
of  the  structure,  it  was  suggested  to  suspend  the  footwalks  from  the  canti- 
lever brackets  that  carry  the  roadways.  This  would  necessitate  small 
roofs  to  protect  pedestrians  from  the  roadway  drippings.  The  arrange- 
ment described  was  shown  by  cost  estimates  to  be  exceedingly  economical, 
but  it  was  objected  to  on  account  of  its  interfering  with  the  running  of 
certain  small  craft  under  the  swing  span. 


132  ECONOMICS    OF   BRIDGEWORK  Chapter  XVI 

Class  No.  6  represents  a  veiy  good  arrangement  which  can  be  modified 
to  suit  nearly  any  conditions  of  combined  traffic.  A  good  example  of  this 
type  is  the  author's  bridge  over  the  Missouri  River  at  Kansas  City,  Mo., 
owned  by  the  Union  Depot,  Bridge,  and  Terminal  Railroad  Company, 
and  known  as  the  Fratt  Bridge. 

In  designing  combined  bridges  of  all  classes  except  No.  1,  a  considerable 
economy  of  metal  may  be  effected  legitimately  by  keeping  the  total  live 
load  for  trusses  as  low  as  is  proper  with  reference  to  the  theory  of  probabili- 
ties. For  instance,  in  Class  No.  2  or  Class  No.  5  the  live  load  for  trusses 
may  be  determined  by  adding  to  the  equivalent  uniform  live  load  for  the 
steam-railway  tracks,  given  by  the  diagram  in  Fig.  6e  of  "Bridge  Fngineer- 
ing,"  a  much  lighter  highway  floor  load  per  lineal  foot  of  span  than  that  pre- 
scribed in  the  specifications;  because  when  the  greatest  train  load  is  on  the 
bridge,  the  chance  of  having  simultaneous^  a  heavy  highway  live  load  is 
very  small.  The  longer  the  span  the  smaller  may  the  live  load  per  square 
foot  of  floor  be  taken  when  finding  the  total  live  load  for  the  trusses.  Again , 
in  Classes  No.  3  and  No.  4  it  would  be  legitimate  to  take  the  truss  live  load 
per  Kneal  foot  for  the  railway  equal  to  twice  the  car  load  per  lineal  foot,  and 
add  thereto  a  small  highway  live  load  as  in  the  last  case.  Finally,  in  Class 
No.  6  in  case  of  a  four-track  bridge  with  cantilevered  highways  and  foot- 
walks,  it  would  be  proper  to  assume  the  live  load  for  the  trusses  equal  to  the 
sum  of  the  car  loads  per  lineal  foot  on  the  four  tracks  and  ignore  entirely 
the  vehicular  and  pedestrian  loadings;  for  the  greatest  probable  live 
load  from  all  classes  of  loading  would  never  exceed  the  said  four  car 
loads. 

This  reduction  of  live  load,  however,  can  readily  be  carried  to  extremes, 
as  was  the  case  in  the  jBrst  accepted  design  of  the  great  cantilever  bridge 
over  the  St.  Lawrence  River  near  Quebec,  and  as  is  likely  to  be  the  case 
whenever  the  preparation  of  the  specifications  for  a  bridge  is  left  either 
directly  or  indirectly  to  the  contractor  who  is  to  build  the  structure.  Good 
judgment,  uninfluenced  in  any  way  by  considerations  of  personal  gain  or 
by  motives  of  false  economy,  should  rule  in  the  estabUsliment  of  the  hve 
loads  for  the  trusses  of  "combined"  bridges. 

It  is  very  seldom  that  the  designing  engineer  of  a  bridge  has  an  oppor- 
tunity to  economize  by  the  manipulation  of  unit  stresses,  because  ordinarily 
he  employes  standard  bridge  specifications;  and  truly  it  is  better  for  him  to 
do  so,  for  the  reason  that  this  question  has  already  been  very  thoroughly 
threshed  out;  but,  as  will  be  explained  presently,  in  certain  structures,  such 
as  trestles,  he  may  have  an  opportunity  to  employ  his  judgment  in  the 
determination  of  unit  stresses  for  certain  unusual  but  possible  combina- 
tions of  loads. 

In  modern  specifications  the  aim  is  to  liavo  a  fixed  unit  stiess  for  each 
kind  of  matei-ial  for  all  l)ut  oxtraoi-dina-ry  ('()m1)iiuitions  of  loads.  In  metals 
it  is  generally  proper  to  place  the  ordinary  intensity  of  working  stress  at 
one-half  of  the  elastic  limit  of  the  material;  but  with  high-alloy  steels  it 


ECONOMICS   OF  LOADS  AND  UNIT  STRESSES  133 

should  not  exceed  one-third  of  the  ultimate  strength.  This  restriction 
applies  mainly  to  heat-treated  eye-bars. 

Some  engineers  deem  it  good  practice  on  the  score  of  economy  to  use 
high-carbon  steel  for  reinforcing-bars;  but  the  author  is  opposed  to  this 
for  two  reasons;  first,  such  metal  is  liable  to  crack  when  being  bent  cold  in 
the  field;  and,  second,  a  high  intensity  of  working  stress  on  the  bars  tends 
to  permit  the  formation  of  cracks  in  the  concrete  in  their  vicinity. 

Very  infrequent  loads  will  permit  overstresses,  or,  in  other  words,  en- 
croachment on  the  factor  of  safety.  A  future  increase  of  live  loads  will 
affect  differently  different  portions  of  a  bridge.  This  is  sometimes  allowed 
for  by  reducing  the  unit  stresses  on  certain  members;  but  it  is  better  to 
design  the  structure  so  that  an  increase  of  loading  of  fifty  per  cent  will 
not  overstress  any  member  more  than  fifty  per  cent. 

Some  designers  specify  abnormally  heavy  loadings  and  correspondingly 
greater  unit  stresses.  This  gives  well  balanced  structures;  but  the  method 
is  illogical,  and  it  has  a  tendency  to  deceive.  If  such  a  practice  were  to 
become  established,  there  would  be  a  liability  on  the  part  of  inexperienced 
engineers  to  employ  high  unit  stresses  with  normal  loads,  which  would  be 
dangerous  or  at  least  ultimately  uneconomic. 

In  very-long-span  bridges  the  selection  of  live  loads  and  unit  stresses  is 
of  extreme  importance ;  because  a  small  legitimate  increase  in  unit  stresses 
or  a  small  reduction  of  loading  may  result  in  a  comparatively  large  saving 
in  cost,  due  to  decrease  of  dead  load. 

If,  for  the  sake  of  either  a  real  or  an  imaginary  economy,  an  increase  in 
unit  stresses  must  be  adopted,  it  is  better  to  make  it  frankly  in  the  main 
members,  where  the  danger  from  overstress  is  least ;  and  then  the  fact  of  the 
existence  of  this  condition  will  be  apparent.  But  if  skimping  were  done  in 
the  detailing,  there  might  easily  be  developed  weaknesses  of  such  a  serious 
nature  as  eventually  to  cause  disaster.  Again,  more  money  can  be  saved 
by  reducing  the  sectional  areas  of  main  members  than  by  trimming  the 
details. 

In  the  designing  of  ordinarj^  truss  bridges,  the  computer  has  practically 
no  choice  as  to  how  the  various  stresses  which  he  figures  are  to  be  com- 
bined, because  the  standard  specifications  by  which  he  is  governed  indicate 
the  method  very  clearly;  but  in  structures  unusual  as  to  either  tj^pe  or 
magnitude  and  in  trestles  the  designer  should  have  some  option  in  making 
the  combinations.  No  hard-and-fast  rule  can  well  be  given  to  cover  all 
cases  of  spans  of  unusual  size  and  character;  except  to  state  that  the 
engineer  should  employ  his  best  judgment  in  relation  to  possibilities  and 
probabilities,  stressing  the  standard  amount  for  combinations  that  are 
likely  to  occur  and  increasing  the  intensities  of  working  stresses  as  the 
combinations  considered  become  more  and  more  improbable  of  realization, 
up  to  the  limit  of  an  excess  of  fifty  (50)  per  cent. 

In  bridges  proper,  with  the  exception  of  arches  having  less  than  three 
hinges,  the  only  unusual  combination  is  that  of  the  ordinary  stresses  and  the 


134  ECONOMICS  OF  BRIDGEWORK  Chapter  XVI 

wind  stresses,  to  allow  for  which  standard  bridge  specifications  permit  an 
increase  of  thirty  (30)  per  cent  over  the  regular  intensities  of  working 
stresses;  but  in  trestles  there  may  be  combinations  of  Hve-load,  impact, 
dead-load,  centrifugal-load,  wind-load,  traction-load,  and  temperature 
stresses;  hence  the  computing  of  some  of  the  sections  for  these  structures  is 
a  complicated  matter. 

As  stated  in  the  specij&cations  for  designing  given  in  Chapter  LXXVIII 
of  "Bridge  Engineering,"  the  columns  of  steel  trestles  are  to  be  propor- 
tioned thus: 

First.  For  Hve  load,  unpact,  centrifugal  load,  and  dead  load,  with  the 
usual  intensities. 

Second.  For  Hve  load,  impact,  centrifugal  load,  dead  load,  and  wind 
load  or  traction  load,  with  an  excess  of  thirty  (30)  per  cent  over  the  usual 
intensities. 

Third.  For  live  load,  impact,  centrifugal  load,  dead  load,  wind  load  or 
traction  load,  and  temperature,  with  an  excess  of  forty  (40)  per  cent  over 
the  usual  intensities. 

Fourth.  For  hve  load,  impact,  centrifugal  load,  dead  load,  traction 
load,  and  wind  load,  with  an  excess  of  forty  (40)  per  cent  over  the  usual 
intensities. 

Fifth.  For  hve  load,  impact,  centrifugal  load,  dead  load,  traction  load, 
wind  load,  and  temperature,  with  an  excess  of  fifty  (50)  per  cent  over  the 
usual  intensities. 

The  preceding  combinations  and  excess  percentages  of  intensities  were 
adjusted  after  much  deliberation;  and  their  pubhcation  in  "Bridge  Engi- 
neering" was  the  first  complete  exposition  of  the  matter  ever  made  in  print. 
In  the  preparation  of  specifications  theretofore,  the  question  had  been 
deemed  too  comphcated  for  written  treatment  and  had  been  left  for  settle- 
ment entirely  to  the  judgment  of  each  individual  designer.  A  study  of 
the  preceding  adjustment  will  show  that  the  greater  the  improbability  of 
any  combination  the  greater  the  intensity  of  the  working  stress  adopted. 
The  worst  combination  (which,  really,  never  could  occur)  would  stress  the 
metal  up  to  three-quarters  of  its  elastic-lhnit,  which  is  perfectly  safe  for  an 
occasional  loading.  It  is  much  better  to  take  into  account  all  possible 
combinations  and  to  stress  the  metal  high  for  the  worst  summation  than  to 
ignore  such  combinations  entirely  and  trust  to  luck  that  they  will  never 
occur,  as  is  too  generally  done  in  trestle  designing.  On  the  other  hand, 
though,  it  would  be  extiavagant  practice  to  combine  all  the  possible 
stresses  and  use  either  the  ordinary  intensities  or  even  these  increased  by 
the  usual  thirty  per  cent  allowance  for  the  inclusion  of  wind.  Trestle 
proportioning  hith(M-to  has  been  rather  unscientific,  and  it  is  to  be  hoped 
that  it  will  soon  b(;  improved.  When  all  is  said  and  done,  however,  it  is 
impi;i(rti(';il)]('  to  eliminate  entirely  individual  judgnK^it  in  the  designing  of 
high  steel  trestles,  because  in  some  cases  local  considerations  will  i)ermit  of 
the  retluction  or  even  the  ignoiing  of  certain  stresses.     For  instance, 


ECONOMICS  OF  LOADS  AND   UNIT  STRESSES  135 

when  a  trestle  is  situated  near  the  middle  of  a  sharp  curve  or  near  the  apex 
of  two  heavy,  rising  grades,  it  would  be  bad  judgment  to  assume  a  high 
velocity  of  train  when  finding  the  stresses  due  to  centrifugal  loading. 

The  combination  of  stresses  in  cantilever  bridges  and  in  arches  is  not 
so  compHcated  as  it  is  in  trestles;  but  it  is  to  be  noted  that  the  sections  of 
members  do  not  need  to  be  increased  because  of  erection  stresses,  unless 
such  total  stresses  (including  those  from  wind  under  an  assumed  probable 
pressure  of  ten  (10)  or  fifteen  (15)  pounds  per  square  foot)  raise  the  inten- 
sities on  the  computed  sections  above  those  specified  for  a  combination  of 
the  usual  loads  with  wind. 

In  summing  up  stresses  care  must  be  taken  to  add  only  those  that  can 
act  simultaneously,  because  some  stresses  can  never  occur  together;  for 
instance,  live  load  and  erection  stresses  in  cantilevers  and  in  arches  erected 
by  cantilevering,  and  hve  load  and  wind  stresses  in  highway  bridges. 
This  word  of  warning  seems  almost  unnecessary;  nevertheless  a  careless 
computer  is  liable  to  smn  up  stresses  that  cannot  act  together,  as  the 
author  knows  from  personal  experience. 

At  the  present  time  there  is  a  division  of  opinion  among  bridge  specialists 
concerning  the  combination  of  stresses  of  opposite  kinds,  some  of  them  going 
so  far  as  to  ignore  altogether  the  effect  of  reversing  stresses.  Until  good 
reason  is  offered  for  making  a  change,  the  author  intends  to  adhere  to  the 
method  which  he  advocates  in  "Bridge  Engineering."  It  is  as  follows: 
If  the  cause  of  the  reversal  be  wind,  the  effect  of  reversion  is  ignored, 
because  not  only  is  there  generally  a  long  interval  between  reversals,  but 
also  the  maximum  wind  stress  on  any  piece  is  of  infrequent  occurrence. 
Reversals  due  to  live  loads  combined  with  impact  are  divided  into  two 
classes;  first,  those  which  occur  in  succession  during  the  passage  of  a  live 
load  over  the  structure,  and,  second,  those  which  are  caused  by  different 
loadings.  In  the  first  case,  each  of  the  two  kinds  of  stress  is  to  be  increased 
by  seventy-five  (75)  per  cent  of  the  other,  then  the  section  required  for 
each  combination  is  to  be  computed  and  the  larger  of  the  two  adopted.  In 
the  second  case  the  procedure  is  similar  to  that  just  described,  except  that 
the  percentage  to  be  added  is  fifty  (50)  instead  of  seventy-five  (75) .  The 
author  does  not  deny  that  it  might  be  perfectly  safe  to  reduce  these  per- 
centages to  fifty  (50)  and  twenty-five  (25),  respectively,  but  he  is  decidedly 
averse  to  ignoring  altogether  the  effect  of  reversion. 

In  any  case  it  would  require  some  exceedingly  strong  evidence  to  induce 
him  to  change  his  method  of  computing  the  number  of  rivets  for  connecting 
main  members,  viz.,  to  add  together  without  any  reduction  the  two  stresses 
of  opposite  kinds  and  proportion  for  the  sum.  Stress  reversal  is  certainly 
harder  upon  the  connecting  rivets  than  upon  the  members  themselves 
which  they  join. 

After  all,  this  controversy  about  the  proper  allowance  for  reversal  of 
stress  may  amount  to  much  ado  about  nothing,  because,  as  pointed  out  in 
Chapter  XI,  the  difference  in  the  weights  of  metal  in  two  continuous-truss 


136  ECONOMICS   OF  BRIDGEWORK  Chapter  XVI 

spans  of  775  feet  each,  when  for  all  reversals  an  addition  of  seventy-five 
(75)  per  cent  of  each  stress  to  the  other  stress  was  made,  and  when  the  effect 
of  reversion  was  entirely  ignored,  was  only  two  and  a  half  (2|)  per  cent. 
Of  this  one  and  a  half  (H)  per  cent  were  due  directly  to  the  increase  in  the 
sections  of  the  pieces  in  which  reversion  occurred,  and  one  (1)  per  cent  to 
the  augmented  dead  load.  Such  being  the  case,  and  in  view  of  our  Imiited 
knowledge  concerning  the  wearing  effects  of  stress  reversal,  it  seems  hardly 
worth  while  at  present  to  make  any  change  in  the  practice  prescribed  in 
''Bridge  Engineering."  On  the  other  hand,  though,  to  be  perfectly  fair, 
it  should  be  pointed  out  that  reversal  of  stress  may  have  a  greater  effect  on 
some  other  kinds  of  bridges,  such  as  arches,  than  it  does  on  continuous- 
truss  structures. 

Until  the  appearance  of  the  January,  1920,  issue  of  the  Bulletin  of  the 
American  Railway  Engineering  Association,  no  writer  of  bridge  specifica- 
tions, as  far  as  the  author  knows,  had  ever  attempted  to  specify  intensities 
of  working  stresses  for  combinations  of  Hve  and  dead  load  stresses  with 
secondary  stresses.  In  the  Report  of  "Committee  XV — on  Iron  and  Steel 
Structures"  (of  which,  by  the  way,  the  author  is  a  member),  published  in 
that  issue,  there  appears  the  following  clause,  numbered  47 : 

Secondary  Stresses: 

Designing  and  detailing  shall  be  done  so  as  to  avoid  secondary  stresses  as  far  as 
possible.  In  ordinary  trusses  without  subpaneling,  no  account  usually  need  be  taken 
of  the  secondary  stresses  in  any  meml^er  whose  width,  measured  in  the  plane  of  the  truss, 
is  less  than  one-tenth  of  its  length.  Where  this  ratio  is  exceeded,  or  where  subpaneling 
is  used,  secondary  stresses  due  to  deflection  of  the  truss  shall  be  computed.  The  unit 
stresses  specified  in  Article  38  may  be  increased  one-third  for  a  combination  of  the 
secondary  stresses  with  the  axial  stresses. 

This  allowance  of  thirty-three  and  a  third  per  cent  applies  only  to  com- 
binations of  live  load,  centrifugal  load,  impact,  and  dead  load  with  second- 
ary stresses;  but  if  other  loadings,  such  as  wind  loads,  traction  loads,  and 
temperature  effects,  are  added  to  the  combination,  the  increment  of  inten- 
sity ought  to  be  increased,  according  to  the  designer's  judgment,  up  to  a 
limit  of  fifty  per  cent. 

Th('i(!  is  an  important  (question  now  before  the  engineering  profession 
for  s(!ttlement,  which,  strictly  speaking,  is  one  of  economics,  viz.:  the 
proper  relation  between  intensities  of  working  stresses  for  bridge  members 
in  tension  and  coin])ression.  In  the  author's  opinion,  there  is  no  valid 
r(;as(>n  for  the  drastic  cut  in  compression  intensities  made  of  late  in  bridge 
specifications  hy  seveial  of  1  \\v  leading  technical  societies.  Concerning  this 
question  h(;  wrote  b)r  tlie  Jan.  IG,  1919,  issue  of  Engineering  Neivs  Record 
the  fcjllowing  communication: 

Tlio  report  of  the  Committee  on  Column  Tests  of  the  American  Society  of  Civil 
EngiiKMTH  aiipoMTs  to  hav(i  caused  som(^  fright  among  ])ridgo  designee's;  for  I  notice 
th;i,t  the  Engineering  Tnstifute  of  Cnnada  has  lately  puhlisluHi  a  "Ceiiernl  Siiecification 
for  Stcicl  Rail\v;iy  Bridges"  in  which  the  unit  stress  for  columns  is  given  by  the  formula, 

7>  =  12,000 -n.3  (//r)2, 


ECONOMICS    OF    LOADS    AND    UNIT   STRESSES  137 

in  which  Z  =  the  unsupported  length  of  the  column  in  inches  and  r  =  its  least  radius  of 
gyration  in  inches. 

This  is  quite  a  sudden  jump  from  the  old  standard  formula, 

p  =  m,000- 60  l/r 

The  -change  indicates  one  of  two  things :  Either  that  hitherto  we  have  been  over- 
stressing  compression  members  15  to  25  per  cent,  or  that  there  is  going  to  be  wasted  a 
vast  quantity  of  metal  in  the  future. 

Moreover,  in  making  such  a  sweeping  change  in  the  compression  formula,  the 
writers  of  the  Canadian  specifications  were  not  consistent,  because  in  Clause  47  they 
allow  for  the  compression  flanges  of  beams  an  intensity  of 

16,000-200  i/&. 

In  the  case  of  railway  stringers  l/b  is  generally  in  the  neighborhood  of  10;  hence  the 
intensity  of  working  stress  is  about  14,000  lbs.  As  b  is  equal  to  about  4.5  r,  for  l/b  =  10 
we  shall  have  ^/r  =  45.     Substituting  this  in  the  Canadian  column  formula  gives 

p  =  12,000'-0.3  (45)2  =  11,400  lbs. 

In  the  case  of  one  compression  member  of  a  bridge,  it  appears  to  be  legitimate  to  stress 
the  metal  up  to  14,000  lbs.  per  square  inch,  and  in  another  up  to  only  11,400  lbs.  per 
square  inch,  a  difference  of  23  per  cent.  And  there  is  no  valid  reason  for  stressing 
differently  a  strut  which  forms  a  part  of  the  top  chord,  of  a  truss  and  a  strut  which 
forms  a  part  of  the  top  flange  of  a  beam.     ' 'Consistency,  thou  art  a  jewel!" 

If  the  correctness  of  the  formula  for  compression  flanges  of  beams  be  conceded — 
a  formula  which,  for  a  dozen  years  or  more,  has  been  one  of  the  clauses  of  the  American 
Railway  Engineering  Association's  standard  bridge-specifications,  and  which  the  Engi- 
neering Institute  of  Canada  has  appropriated  without  change — and  if  it  be  granted 
that  b  is  generally  equal  to  about  4.5  r — why  should  not  the  equivalent  formula, 

p  =  16,000- 45  Z/r, 

apply  in  general  to  struts  with  fixed  ends?  Be  it  noticed  that  this  formula  gives  higher 
results  than  does  my  old  formula, 

73  =  16,000-60  Z/r. 

The  American  R,ailway  Engineering  Association  is  getting  ready  to  trim  down 
materially  its  old  intensities  for  steel  struts,  although  not  to  the  extent  that  the  Engi- 
neering Institute  of  Canada  has  done.* 

What  aggravates  the  effect  of  this  proposed  decrease  of  compression  intensities 
is  that,  simultaneously  therewith,  the  American  Railway  Engineering  Association  is 
contemplating  increasing  its  tensile  intensity  of  working  stress  from  16,000  lbs.  to  18,000 
lbs.;   and  other  specification  writers  are  advising  that  it  be  made  as  high  as  20,000  lbs. 


*  The  1920  A.  R.  E.  A.  bridge  specifications  permit  the  following  intensities  of 

working  compressive  stresses : 

I 

Struts 15,000-50  -  but  not  to  exceed  12,500  lbs. 

r 

I 

Flanges  of  girders 14,000-200  -. 

b 

The  previous  strut  formula  of  the  A.  R.  E.  A.  was  16,000—70  — ;  hence  the  new 

r 
I 
formula  gives  lower  results  when  —  is  less  than  50  and  higher  results  when  it  is  greater. 


138  ECONOMICS    OF   BRIDGEWORK  Chapter  XVI 

To  an  outsider  it  must  look  as  if  the  bridge  engineers  of  this  country  were  losing  their 
heads! 

The  compression  tests  that  started  the  present  wave  of  apprehension  did  not  have 
governing  conditions  corresponding  properly  to  those  of  actual  truss-members;  hence 
I  would  suggest  that,  before  the  bridge  engineers  of  America  take  the  drastic  step  of 
assuming  steel  in  compression  to  be  only  60  or  70%  as  strong  as  the  same  material  in 
tension,  some  really  practical  tests  of  struts  be  made  under  conditions  corresponding 
to  those  in  actual  structures.  Such  a  series  of  tests  would  cost  considerable  money; 
but,  if  the  Bin-eau  of  Standards  at  Washington  were  to  indorse  the  suggestion  to  make 
them,  it  ought  not  to  be  at  all  difficult  to  obtain  from  Congress  an  ample  appropriation 
for  the  purpose. 

The  method  of  conducting  these  tests  that  I  have  in  mind  is  this: 

Let  there  be  built  a  five-panel,  riveted-truss  bridge  of  about  100-ft.  3pan;  let  the 
middle  panel-lengths  of  the  top  chords  thereof  be  made  decidedly  weaker  than  all  the 
other  portions  of  the  structure;  and  let  a  uniformly-distributed  live-load  be  applied 
at  the  panel-points  by  hydraulic  pistons.  All  portions  of  the  structure,  including 
the  two  weak  members,  should  be  scientifically  detailed,  so  that  failure  will  inevitably 
take  place  in  the  main  portions  of  the  weak  struts  and  not  in  the  details  thereof,  and 
so  that  the  bridge  can  be  used  for  a  long  series  of  tests  to  destruction  of  the  said  mid- 
panel  lengths  of  the  top  chords.  The  weak  members  should  be  attached  to  the  con- 
necting plates  with  an  ample  number  of  rivets  to  develop  the  full  strength  of  the  test 
pieces;  and  these  rivets  should  be  removed  carefully  after  each  test  to  destruction  is 
completed. 

Of  course  it  would  be  entirely  practicable  to  vary  the  value  of  Z/r  in  the  different 
tests,  provided  that  the  attachment  of  the  test-strut  be  not  made  eccentric. 

There  should  be  a  supporting  platform  beneath  the  span  to  prevent  its  falling  any 
material  distance  when  failure  occurs. 

By  adopting  a  weak  vertical  post  instead  of  a  weak  panel-length  of  top  chord,  and 
by  loading  (at  the  elevation  of  the  latter)  three  panel-points  only,  a  series  of  tests  could 
be  made  on  vertical  posts.  A  similar  series  could  be  carried  out  on  the  inclined  end 
posts. 

A  cheaper  method  than  that  just  described,  but  not  quite  as  satisfactory,  would  be 
to  build  a  single  truss,  instead  of  the  complete  span,  and  steady  it  laterally  but  not 
vertically,  and  then  to  apply  the  test  loadings  directly  above  the  top  chord  at  the  panel- 
points.  A  great  advantage  of  the  span  tests  as  compared  with  the  truss  tests  is  that 
duplicate  tests  could  be  Tnade  simultaneously  on  similar  members.  Moreover,  the  span 
tests  would  be  in  practically  exact  accord  with  actual  conditions  of  loading,  while  the 
truss  tests  would  not. 

By  removing  occasionally  the  test  loading,  the  elastic  limits  of  the  struts  could 
be  ascertained  through  noting  the  absence  or  otherwise  of  permanent  set. 

Experiments  similar  to  those  described  could  be  made  on  a  pin-connected  span  or  a 
pin-connected  truss  so  as  to  determine  the  strength  of  struts  with  hinged  ends. 

In  view  of  the  immense  amount  of  bridge  manufacture  and  construction  that  is 
likely  to  be  done  in  the  United  States  within  the  next  five  or  ten  years,  the  making  of 
this  proposed  series  of  tests  is  worthy  of  being  considered  a  matter  of  national  impor- 
tance. 

In  order  to  elaborate  the  preceding  communication,  the  author  had  his 
associate  engineer,  F.  H.  Frankland,  Member  American  Society  Civil 
Engineers,  write  another  letter  to  Engineering  News-Record  embodying 
certain  subsequent  thoughts  upon  the  details  of  the  proposed  series  of 
experiments,  which  letter  was  published  in  the  issue  of  March  6,  1919.  It 
reads  as  follows: 


ECONOMICS   OF   LOADS   AND   UNIT   STRESSES  139 

With  reference  to  the  matter  of  formulae  for  steel  columns,  dealt  with  in  recent 
articles  and  letters  appearing  in  Engineering  News-Record,  the  writer  wishes  to  take 
this  opportunity  of  drawing  attention  to  the  fact  that  existing  column  formulae  are  not 
founded  on  really  proper  tests,  and  that,  therefore,  engineers  should  not  rest  satisfied 
until  such  proper  tests  have  been  made,  and,  from  the  empirical  rules  deduced  there- 
from, a  really  sound  column  formula  has  been  evolved. 

No  column  experiments  have  yet  been  made  which  conform  to  actual  conditions 
existing  in  modern  bridges,  as  very  few  columns  nowadays  have  hinged  ends,  and  flat- 
end  tests  are  likely  to  be  very  deceptive,  because  of  corner  bearing. 

The  opinion  expressed  by  Mr.  Charles  E.  Fowler  in  his  letter  on  page  343  of  your 
issue  of  Feb.  13,  1919,  to  the  effect  that  a  straight-line  formula  is  to  be  desired  on  account 
of  its  simplicity,  is  to  be  commended,  as  there  is  every  probability  that  a  satisfactory 
straight-line  formula  can  be  derived  from  proper  tests.  It  is  to  be  noted  that  some  of 
the  formula)  given  by  Mr;  Fowler  in  his  letter  use  the  {l/rY,  this  being  a  holdover 
from  the  old  Euler  formula,  which  was  established  for  greater  values  of  l/r  than  are 
used  in  practice. 

With  reference  to  Dr.  Waddell's  scheme  for  testing  top-chord  members  by  means  of 
experiments  conducted  on  a  specially-built,  full-size  bridge,  the  writer  begs  to  make 
the  following  suggestions  for  a  practical  method  for  maJcing  such  tests:  Build  a  single- 
track.  Class  70,  through -truss  bridge,  with  the  weak  member  designed  for,  say,  Class  40 
loading,  so  that  the  destruction  of  the  weak  member  could  be  accomplished  without 
injury  to  the  rest  of  the  structure,  thus  facilitating  repairs  for  repeated  tests.  The 
connection  plates  for  the  weak  members  should  be  extra  strong.  After  the  compression 
tests  are  completed,  a  series  of  corresponding  tests  on  tension  members  should  be 
made,  so  as  to  determine  the  real  efficiencies  of  both  tension  and  compression  members 
and  their  comparative  strengths.  Unless  this  kind  of  a  test  be  carried  out,  we  shall 
never  have  any  really  reliable  test  data,  as  the  existing  data  are,  to  a  great  extent,  mis- 
leading.    It  is  advisable  that  more  than  one  value  of  l/r  should  be  tested  for. 

It  should  not  be  overlooked,  in  making  up  a  design  for  a  test  structure,  that  there 
is  a  necessity  for  thorough  detailing  throughout,  especially  in  connection  with  the 
weak  members,  so  that  failure  will  be  in  the  form  of  a  square  break  instead  of  being 
due  to  any  insufficient  detail,  thus  removing  ambiguity.  It  would  be  advisable  to  build 
the  permanent  members  of  the  trusses  of  the  test  bridge  of  nickel  steel,  so  that  the 
permanent  and  the  weak  sections  would  be  somewhat  alike,  if  the  weak  section  were  of 
the  ordinary  structural  grade  of  carbon  steel. 

.  The  most  satisfactory  method  of  applying  the  load  would  be  by  means  of  hydraulic 
presses  or  jacks,  to  be  applied  at  panel  points,  and  all  connected  so  that  the  load  would 
be  uniform.  Pressure  records  should  be  automatically  made.  Control  of  the  applied 
load  by  this  means  would  be  very  simple  and  positive.  It  would  be  desirable  to  make 
tests  for  low  values  of  l/r,  so  as  to  establish  the  necessity  or  otherwise  for  limiting  inten- 
sities of  working  i^tress. 

Many  of  the  tests  we  are  relying  on  at  the  present  time  for  our  formulae  were  made 
on  badly  designed  struts;  and  I  venture  to  say  that  tests  on  properly  designed  struts 
would  show  up  stronger  than  the  present  tendency  of  the  profession  in  strut  design 
indicates. 

If  the  series  of  tests  above  suggested  were  thoroughly  carried  out,  the  engineering 
profession  would  possess  some  authentic  knowledge  concerning  the  actual  strengths  of 
both  tension  and  compression  members  in  bridges,  and  a  large  amount  of  guess  work 
would  be  avoided  in  future  constructions. 

As  yet  no  steps  have  been  taken  to  materialize  this  suggestion  of  the 
author's.  Probably  the  profession  will  say  that  it  is  up  to  him  to  see  that 
his  proposed  tests  are  made;  and,  possibly,  after  this  treatise  is  com- 
pleted and  launched,  he  will  find  time  to  make  an  attempt  to  induce  the 


140  ECONOMICS   OF   BRTDGEWOKK  Chapter  XVI 

Federal  Government  to  undertake  the  said  tests  through  the  Bureau  of 
Standards. 

The  matter  of  allowmg  higher  intensities  of  working  stresses  for  old 
bridges  in  service  than  those  specified  for  the  designing  of  new  structures 
is  treated  at  length  in  Chapter  XLI  on  "Economics  of  Maintenance  and 
Repairs." 


There  is  an  economic  question  concerning  loads  to  which  but  little 
attention  has  hitherto  been  paid,  viz.,  the  best  way  to  compute  the  total 
loading  for  a  foundation  pile.  Most  engineers  ignore  impact  altogether  in 
estimating  the  load  on  piles  supporting  piers  of  bridges  and  trestles,  and  the 
author  has  often  done  so;  but  there  are  cases  in  which  such  practice  might 
be  unsafe.  An  instance  of  this  kind  occurred  in  a  competitive  study  made 
by  the  author  in  relation  to  the  rebuilding  of  the  Galveston  Causeway 
after  a  large  portion  of  it  had  been  destroyed  during  a  hurricane  accom- 
panied by  a  tidal  wave.  There  the  piles  were  comparatively  short;  and 
they  passed  through  a  thick  layer  of  very  soft  material  before  reaching  a 
somewhat  firmer  one.  The  layout  under  consideration  was  one  of  rein- 
forced-concrete  girders;  hence  the  spans  had  to  be  short  and  the  piers  small. 
Under  such  conditions  the  vibration  from  passing  trains  certainly  would 
have  reached  the  piles  from  the  spans  with  comparatively  little  diminution 
in  effectiveness;  hence  it  was  essential  to  allow  for  impact  on  the  said 
piles.  They  had  to  be  proportioned  also  for  effect  of  thrust  of  braked 
trains;  but,  as  the  thrust  would  have  been  exerted  when  the  train  speed 
was  slowing  down,  it  would  not  have  been  logical  to  combine  the  thrust- 
effect  with  the  full  value  of  impact.  That  was  an  instance  where  the  con- 
sulting engineer's  judgment  had  to  be  relied  upon  to  determine  the  proper 
combination  of  loads,  and  where  a  familiarity  •  with  the  principles  of  true 
economics  would  be  of  great  value  to  the  owners. 

The  reason  why  the  impact  on  foundation  piles  may  either  be  assumed 
comparatively  small,  or  possibly  ignored  altogether,  are  as  follows: 

First.  If  allowed  for  at  all,  the  impact  should  be  assumed  for  a  span- 
length  equal  to  the  sum  of  the  lengths  of  the  two  spans  which  the  pier  under 
consideration  helps  to  support. 

Second.  The  impacts  given  by  formula  for  any  span  are  the  greatest 
that  can  come  upon  any  main  truss-member  thereof,  and  are  much 
larger  than  those  for  the  span  as  a  whole,  as  indicated  by  the  ratio  of  mid- 
span  d(!fl(;ctions  under  the  same  load  when  moving  and  when  quiescent. 

Third.  The  critical  speed  which  produces  the  impact  given  liy  foinuila 
is  likely  to  Ix;  d(^v(!loped  very  seldom,  if  at  all,  on  any  ])articular  bridge. 

Fourth.  Th(!  massiv(Miess  of  the  pier  will  absorb  some  of  the  shock  that 
reaches  its  top  befor(>  the  said  shock  i)asses  to  th(>  base. 

Fifth.  As  the  to]is  of  the  ])iles  are  (Micased  in  \\\v  mass  of  concrete,  they 
will  act  together  as  a  unit  and  thus  k^ssen  somewhat  the  impact  ])er  pile. 


CHAPTER  XVII 

ECONOMICS   OF  TIME   AND   MONEY   IN   MAKING   COST-ESTIMATES   FOR 

BRIDGES 

One  of  the  author's  fundamental  motives  in  writing  "Bridg3  Engineer- 
ing" was  to  provide  bridge  speciaHsts  with  a  means  of  estimating  quite 
accurately,  and  at  the  same  time  very  quickly,  the  costs  of  substructure, 
superstructure,  and  approaches  for  any  kind  of  bridge  upon  which  they  are 
ever  likely  to  have  to  figure.  Rather  to  his  surprise,  the  numerous  review- 
ers of  the  work  almost  entirely  overlooked  this  important  characteristic  of 
the  treatise.  As  it  is  one  of  the  most  valuable  features  thereof,  the  author, 
in  order  to  make  known  this  special  usefulness,  drafted  a  set  of  four  prob- 
lems for  solution,  solely  by  means  of  the  curves  of  quantities,  tables,  for- 
mulae, and  other  information  scattered  throughout  the  book;  and  arranged 
for  a  series  of  competitions  among  the  senior  students  in  a  number  of  tech- 
nical schools,  and  afterwards,  by  a  comparison  of  the  marks  resulting  from  a 
pre-arranged  system  of  grading,  effecting  a  competition  among  the  said 
schools  themselves  by  comparing  in  the  columns  of  the  technical  press  the 
sums  of  the  marks  of  the  three  prize  winners  in  each  school.  The  judges 
were  appointed,  and  the  system  of  marking  was  fixed,  all  ready  for  the 
comparison  of  the  unsigned  competitive  papers ;  but  the  entering  of  Amer- 
ica into  the  Great  War  so  upset  the  technical  students  all  over  the  country 
that  the  competition  had  to  be  abandoned.  The  author  is  ready  to  provide 
the  promised  prizes  (books  of  no  great  financial  worth,  but  valuable  as 
souvenirs  of  success  in  competition),  in  case  that  any  of  the  teachers  of 
engineering  show  a  desire  to  have  the  offer  renewed  for  a  new  set  of  prob- 
lems. As  a  matter  of  possible  interest,  the  original  list  of  questions  is 
reproduced  at  the  end  of  this  chapter;  and  the  author  suggests  that,  for 
the  sake  of  practice  in  quick  computation,  engineering  students  try  their 
wits  on  the  solution  of  them. 

In  the  author's  practice  during  the  last  three  or  four  years  he  has  made 
very  quickly  many  cost  estimates  on  steam-railway,  electric-railway,  high- 
way, and  combined  bridges  by  means  of  the  diagrams,  tables,  and  formulae 
of  "Bridge  Engineering"  for  rolled  I-beam  spans,  plate-girder  spans  (both 
deck  and  half -through) ,  riveted-truss  simple-spans,  pin-connected  simple- 
spans,  swing  spans,  cantilevers,  suspension  bridges,  and  reinforced-con- 
crete  structures;  and  the  results  when  tested  have  been  found  to  be  exceed- 
ingly accurate.  The  estimating  of  costs  of  structures  in  this  manner  is  a 
very  easy  task  compared  with  the  job  of  making  similar  computations 

141 


142  ECONOMICS   OF   BRIDGEWORK  Chapteh  XVII 

before  these  records  were  compiled;  consequently  it  is  to  be  hoped  that 
bridge  engineers  will  soon  learn  to  utilize  properly  the  vast  amount  of 
information  collected  by  the  author  in  his  many  years  of  practice  as  a 
bridge  specialist  and  presented  to  the  engineering  profession  in  his  magnum 
opus. 

The  following  examples  and-their  solutions  will  illustrate  how  the  dia- 
grams are  to  be  used  and  how  quickly  they  give  results: 

Example  No.  1 

What  is  the  weight  of  structural  steel  in  a  single-track,  steam-railway, 
Class  60,  riveted-truss  bridge  built  of  carbon  steel  and  consisting  of  one 
420'  through  span,  two  265',  two  215',  and  two  165'  deck  spans  for  a 
proposed  crossing  of  the  Missouri  River? 

Solution 

From  Fig.  55t  on  p.  1228,  and  Fig.  55/  on  p.  1231  of  B.E.,  we  have  the 
following : 

1  420'  Thro,  span    @  5,450  lbs.  =  2,289,000  lbs. 

2  265'  Deck  spans  @  2,675  lbs.  =  1,418,000  lbs. 
2  215'  "  ''  @  2,060  lbs.  =  886,000  lbs. 
2  165'       "         ''     @  1,620  lbs.  =    535,000  lbs. 


Total  metal  in  superstructure  =  5, 128,000  lbs. 

Example  No.  2 

A  double-track,  steam-railway.  Class  55  bridge,  having  a  total  length  of 
820'  from  end  to  end  of  superstructure,  is  to  be  built  so  close  to  high  water 
that  half -through  plate-girders  will  be  required.  Assuming  that  there  will 
be  10,  11,  12,  or  13  spans  of  equal  length,  what  will  be  the  total  weight  of 
metal  for  each  case? 

Solution 

Ignoring  the  small  spaces  over  piers  between  ends  of  girders,  the  various 
span-lengths  will  be  82,  74.5,  68.3,  and  63.1  feet.  Referring  to  Fig.  55r, 
on  p.  1237  of  B.E.,  we  find  the  following  weights  of  metal  per  lineal  foot  of 
structure;  3,860,  3,700,  3,550,  and  3,420.  The  total  weights  of  metal 
will,  therefore  be, 

3,860  Ibs.X 820  =  3,165,000  lbs. 

3,690  lbs.  X 820  =  3,026,000  lbs. 

3,550  lbs.  X 820  =  2,91 1,000  lbs. 

3,460  Ibs.X 820  =  2,837,000  lbs. 

Example  No.  S 

What  is  the  weight  of  metal  in  a  double-track,  steam-railway,  Class  65, 
pin-connected,  Pratt-truss  bridge,  ))ui]t  of  ('ar])on  stool  and  consisting  of 
five  330'  through  spans? 


TIME    AND    MONEY    IN    MAKING    COST-ESTIMATES    FOR    BRIDGES      143 

Solution 

From  Fig.  5566,  on  p.  1246  of  B.E.,  we  find  the  weight  of  superstructure 
metal  to  be  7,350  lbs.  per  Uneal  foot  of  span;  hence  the  total  weight  of  metal 
will  be, 

5X330X7,350=  12,127,000  lbs. 

Example  No.  4 

What  is  the  total  weight  of  metal  in  a  double-track,  steam-railway, 
center-bearing  swing-span,  350'  long  between  centres  of  end  supports, 
having  riveted  trusses,  and  carrying  a  Class  50  live  load? 

Solution 

From  Fig.  5566,  on  p.  1246  of  B.E.,  we  find  the  weight  of  structural 
steel  per  lineal  foot  of  a  350'  fixed  span  to  be  6,450  lbs.;  and  in  Fig.  55ee 
on  p.  1249  thereof  is  given  83  as  the  percentage  to  apply  for  a  swing  span 
of  that  length  and  the  type  stated ;  hence  the  total  weight  of  metal  will  be, 

6,450  X  0.83  X  350  =  1,874,000  lbs. 

Example  No.  5 

A  540',  riveted,  Petit-truss,  highway  span  with  paved  roadway  on  rein- 
forced concrete  base  and  with  reinforced-granitoid  sidewalks,  for  which  the 
total  live  load  per  Hneal  foot  of  span  for  trusses  is  3,200  lbs.,  has  a  dead 
load,  exclusive  of  weight  of  trusses,  equal  to  7,200  lbs.  per  lineal  foot,  the 
total  clear  width  of  deck  from  out  to  out  being  60'.  What  is  the  weight  of 
carbon  steel  in  the  two  trusses  required  to  carry  this  loading? 

Solution 

From  Fig.  7e,  on  p.  131  of  B.E.,  we  find  the  coefficient  for  impact  with 
^  =  fo^  =  3  to  be  0.05;  hence  each  truss  load  per  lineal  foot,  exclusive  of  its 
own  weight,  will  be  as  follows: 

Live  load  =  |X3,200  lbs =  1,600  lbs. 

Impact  =  0.05X1,600  lbs =      80  lbs. 

Flooring  and  metal  in  floor  and  lateral  sys- 

tems  =  iX7,200  lbs =3,600  lbs. 

Summation =  5,280  lbs. 

Assume  weight  per  foot  of  one  truss  to  be =  3,000  lbs. 

Tentative  total  load  per  lineal  foot  per  truss. ...    =  8,280  lbs. 

Referring  to  Fig.  55/i/i,  on  p.  1252  of  B.E.,  for  a  540'  span  the  8,000  lbs. 
curve  gives  3,100  lbs.  and  the  10,000  lbs.  curve  gives  3,700  lbs.;  hence,  by 


144  ECONOMICS    OF   BRIDGEWORK  Chapter  XVII 

interpolation,  8,280  lbs.  would  give  3,184  lbs.,  showing  that  the  assumed 
truss  weight  of  3,000  lbs.  per  foot  was  too  light.  Let  us  try  3,260  lbs.  mak- 
ing the  total  load  8,540  lbs.  Interpolating  as  before  gives  3,262  lbs.  As 
this  agrees  with  the  assumed  3,260  lbs.,  it  is  correct;  and,  therefore,  the 
total  weight  of  steel  in  the  two  trusses  is 

2X3,262X540-3,523,000  lbs. 

Example  No.  6 

What  is  the  weight  of  metal  in  the  four  shoes  of  a  380'  span,  double- 
track,  steam-railway,  riveted-truss  bridge  for  Class  60  live  load? 

Solution 

From  Fig.  6e,  on  p.  106  of  B.E.,  we  find  the  equivalent  uniform  hve 
load  to  be, 

2X6,830  lbs =  13,660  lbs. 

From  Fig.  7c,  on  p.  129  thereof,  we  find  the  impact  to 

be  18%  or 2,460  lbs. 

From  Fig.  55y,  on  p.  1243  of  same,  we  find  the  weight 

of  metal  per  lineal  foot  of  span  to  be 8,000  lbs. 

Flooring  for  two  tracks,  say 1,000  lbs. 

Total  load  per  lineal  foot  of  span =25,120  lbs. 

Weight  of  span  =  25,120X380 .  .  =9,546,000  lbs. 

Load  on  one  shoe  =  iX9,546,000  lbs =2,386,000  lbs. 

From  Fig.  55mm,  on  p.  1257  of  B.E.,  we  find  the  average  weight  of  one 
shoe  to  be  18,400  lbs.,  hence  the  weight  of  the  four  shoes  is, 

4X18,400  =  73,600  lbs. 

Example  No.  7 

What  is  the  weight  of  metal  per  lineal  foot  of  structure  in  a  single-track, 
steam-railway,  steel  trestle,  170'  high,  to  carry  Class  55  live  load? 

Solution 

From  Fig.  55rr,  on  p.  1262  of  B.E.,  we  find  the  required  weight  to  be 
3,140  lbs. 

Example  No.  8 

What  is  the  average  weight  of  carbon  steel  per  lineal  foot  of  structure  in 
a  double-track,  steam-railway,  riveted-truss.  Type  A,  cantilever-  ])iidge  to 
carry  C'lass  70  live  loading,  the  length  of  main  span,  mcasunnl  from  center 
to  center  of  piers,  being  1140  feet? 


TIME    AND    MONEY    IN    MAKING    COST-ESTIMATES    FOR    BRIDGES      145 

Solution 

From  Fig.  55ccc,  on  p.  1273  of  B.E.,  we  find  the  required  weight  to  be 
20,500  lbs. 

Example  No.  9 

What  is  the  yardage  in  a  concrete  pier  with  rounded  ends  and  a  half- 
inch  batter,  having  no  coping,  the  extreme  top  dimensions  being  8'  and  28' 
and  the  height  52'? 

Solution 

From  Fig.  566,  on  p.  1302  of  B.E.,  we  find  the  yardage  of  the  two 
half-truncated  cones  to  be  160;  and  from  Fig.  56d,  on  p.  1304  thereof,  we 
find  the  yardage  of  a  strip  one  foot  wide  to  be  19.5;  hence  the  total  volume 
will  be 

160+ (28- 8)  X  19.5  =  550  cu.  yds. 

Example  No.  10  ' 

What  is  the  yardage  in  a  column-pedestal  4.5'  square  on  top,  14'  high, 
and  having  a  batter  of  two  inches  to  one  foot? 

Solution 
From  Fig.  56/c,  on  p.  1311  of  B.E.,  we  find  the  volume  to  be  25.2  cu.  yds 

Example  No.  11 

What  is  the  yardage  in  a  wing  abutment  for  a  single-track-railway 
embankment  having  side  slopes  of  one  and  a  half  to  one,  the  vertical  dis- 
tance from  foundation  to  base  of  rail  being  28',  the  height  of  parapet  7', 
that  of  base  2',  that  of  coping  1',  and  that  of  wing  walls  at  ends  14'? 

Solution 

The  height  from  bottom  of  coping  to  top  of  base  will  be  about  17',  the 
greatest  height  of  wing  wall  above  top  of  base  25',  and  the  least  height 
thereof  above  same  12'. 

From  Figs.  56o  and  56p,  on  pp.  1315  and  1316  of  B.E.,  we  find  the  fol- 
lowing 

Volume  of  Parapet,  Coping,  Shaft,  and  Walls  to  end  of 

Parapet 185  cu.  yds. 

Volume  of  Portions  of  Wing  Walls  extending  beyond 
Parapet,   and  above  elevation  of  top  of  Base  = 

190-35 =155  cu.  yds. 

Volume  of  base  to  end  of  Parapet  =  2X 17 =   34  cu.  yds. 

Volume  of  base  beyond  Parapet  =  2(14.2  — 7.2) =    14  cu.  yds. 

Total  volume  of  abutment =  388  cu.  yds. 


146  ECONOMICS   OF  BRIDGEWORK  Chapter  XVII 

These  examples  might  be  continued  so  as  to  include  the  finding  of 
quantities  in  retaining  walls,  both  plain  and  reinforced,  reinforced-concrete 
trestles,  and  reinforced-concrete  arch  bridges,  but  space  wiU  not  permit; 
hence  the  reader  is  referred  for  examples  of  the  estimates  for  such  structures 
to  pages  1317-1347  of  ''Bridge  Engineering." 

Again,  by  employing  the  various  formulae  given  in  Chapter  XXVII 
of  that  treatise,  the  cost  of  any  highway  or  electric  railway  suspension 
bridge  can  be  quickly  estimated.  As  stated  elsewhere  herein,  the  author 
in  a  single  working  day  made  thereby  a  close  estimate  of  cost  for  a  2,500'- 
span,  highway  bridge,  including  substructure,  superstructure,  approaches, 
and  accessory  works,  for  a  proposed  crossing  of  the  Detroit  River  at  the 
City  of  Detroit. 

The  eleven  simple  examples  given  should  suffice  to  illustrate  the  faciUty 
with  which  one  who  is  famihar  with  ''Bridge  Engineering"  can  figure  the 
quantities  of  materials  for  all  ordinary  bridges.  Those  for  other  structures 
can  be  obtained  in  a  similar  manner  by  the  expenditure  of  somewhat  more 
time,  but  still  very  readily. 

The  following  are  the  four  student  problems  referred  to  near  the  begin- 
ning of  this  chapter;  and  the  author  again  suggests  that  they  be  solved  by 
any  young  engineer  who  desires  to  perfect  himself  in  the  art  of  making 
quick  computations  for  costs  of  bridges: 

Problem  A 

The  following  data  for  a  river  crossing  are  supposed  to  be  furnished  by  a 

survey  for  a  double-track,  steam  railway  in  the  northwest  corner  of  the 

state  of  Arkansas: 

Width  of  watershed  at  crossing 36  miles. 

Width  of  same  at  a  distance  of  forty  (40)  miles  up-stream     44  miles. 

Ditto  eighty  (80)  miles  up-stream 28  miles. 

Ditto  one  hundred  and  ten  (110)  miles  up-stream 16  miles. 

Intermediate  widths  are  to  be  directly  interpolated. 

Extreme  length  of  watershed  above  crossing 125  miles. 

Width  of  river  at  a  fairly  low  stage  of  water  when  the 

•survey  was  made 520  feet. 

Maximum  depth  of  water  at  the  same  time  at  a  point 
about  one  hundred  and  ten  (110)  feet  from  the 
water's  edge  on  the  left  bank 5  feet. 

Average  depth  of  water 3.3  feet. 

Greatest  observed  surface  velocity  at  crossing  when  sur- 
vey was  made,  being  the  average  of  four  observa- 
tions        2.55  ft.  per  sec. 

[  three    (3)    vertical 

Side  slope  on  left  bank  where  the  rock  is  exposed j  to  one  (I)  horizon- 

[  tal. 

Height  of  top  of  left  bank  al)ove  water  at  time  of  survey .      15  feet. 


TIME    AND    MONEY    IN    MAKING    COST-ESTIMATES    FOR    BRIDGES       147 

Side  slope  on  the  right  bank  of  the  stream,  from  water's 
edge  to  break  of  bank  (a  distance  of  thirty-five  (35) 

feet) one  (1)  vertical  in  five  (5)  horizontal. 

Height  of  top  of  right  bank  above  surface  of  water  when 

survey  was  made 7  feet. 

Width  of  level  portion  of  top  of  right  bank 80  feet. 

Falling  slope  back  of  right  bank  for  a  distance  of  eight 
hundred  (800)  feet  averages  four-tenths  (0.4)  of  one 
per  cent. 
Then  comes  a  dry,  level  slough,  three  hundred  (300)  feet 
wide;  and,  finally,  there  is  a  rising  grade  of  seven- 
tenths  (0.7)  of  one  per  cent  for  a  distance  of  some 
eighteen  hundred  (1,800)  feet. 
A  profile  of  the  crossing  is  shown  in  Fig.  17a. 

Average  slope  of  river  for  first  ten  (10)  miles  up-stream  is  1.37  feet  per 
mile;  and  in  each  ten-mile  stretch  beyond  it  increases  regularly  by  one 
and  one-tenth  (1.1)  feet  per  mile. 

The  stream  at  times  carries  considerable  drift,  but  there  is  no  proba- 
bility of  the  channel  changing. 

Borings  near  the  water's  edge  on  the  right  side,  at  time  of  survey,  showed 
five  (5)  feet  of  silt,  sixteen  (16)  feet  of  sand,  running  from  fine  at  top  to 
coarse  at  bottom,  then  gravel  very  fine  at  first  but  increasing  in  coarseness 
gradually  with  the  depth,  the  vertical  measurements  being  made  from  the 
elevation  of  the  water. 

Material  of  the  low  bank  and  of  the  flat  is  sandy  loam  covered  with 
vegetation  that  would  offer  considerable  resistance  to  scour.  Across  the 
slough  the  material  is  harder. 

The  crossing  is  near  the  middle  of  a  long,  easy  bend  in  the  stream ;  and 
the  current  at  high  water  impinges  against  the  rocky  bank. 

Highest  water-mark  found  was  about  eight  feet  above  the  water  level 
at  time  of  survey.     No  reliable  records  of  floods  were  obtainable. 

Rainfall  on  watershed  averages  about  fortj^-five  (45)  inches  per  annum. 

Grade  line  on  structure,  twelve  (12)  feet  above  the  extreme  future  high- 
water. 

Clearance  line  for  superstructure,  at  least  four  (4)  feet  above  same. 

Crossing  is  entirely  on  tangent  and,  as  nearly  as  may  be,  at  right  angles 
to  the  current. 

Superstructure  is  to  be  of  steel,  and  substructure  of  concrete. 

Piles  may  or  may  not  be  used  for  foundations. 

The  channel  pier  foundations  must  go  to  a  depth  of  twelve  (12)  feet 
below  greatest  probable  scour  in  case  piles  are  employed,  or  twenty  (20) 
feet  below  same  in  case  that  they  are  not. 

Approaches  are  to  be  of  earth  embankment,  but  it  is  permissible  to  put 
in  some  wooden  pile  trestle  across  the  slough,  if  investigation  should  indi- 
cate it  to  be  necessary. 


148  ECONOMICS    OF   BRIDGEWORK  Chapter  XVII 

There  are  no  restrictions  as  to  span-lengths  or  locations  of  piers,  because 
the  river  is  not  navigable. 

The  type  of  floor  is  the  ordinary  one  of  untreated  wooden  ties  and 
guards  with  eighty  (80)  pound  rails. 

The  live  load  is  Waddell's  Class  60. 

The  following  are  the  costs  of -the  various  materials  delivered  at  site: 

Cement  two  dollars  ($2.00)  per  bbl. 

Broken  stone  and  gravel,  one  dollar  and  fifty  cents  ($1.50)  per  cubic 
yard. 

Sand  (clean  and  ready  for  use),  one  dollar  ($1.00)  per  cubic  yard. 

Timber,  twenty-two  dollars  ($22.00)  per  M.  feet  B.  M. 

Piles,  twenty  (20)  cents  per  lineal  foot. 

Structural  steel,  4.5  cents  per  pound  for  truss  spans  and  4.2  cents  per 
pound  for  plate-girder  spans. 

Rails,  forty-two  dollars  ($42.00)  per  long  ton. 

The  following  are  the  schedule  costs  of  the  erection  work: 

Sinking  of  pneumatic  caissons,  five  dollars  ($5.00)  per  cubic  yard. 

Sinking  by  open-dredging,  three  dollars  and  fifty  cents  ($3.50)  per  cubic 
yard. 

Driving  piles  for  trestle,  twenty  (20)  cents  per  lineal  foot. 

Driving  piles  for  foundations,  forty  (40)  cents  per  lineal  foot. 

Erection  of  metal,  including  cost  of  falsework  and  painting,  1.2  cents  per 
pound  for  truss  spans  and  0.8  cent  per  pound  for  plate-girder  spans. 

The  problem  is  to  determine  the  extreme  high-water  profiles  both  before 
and  after  the  structure  is  completed,  to  make  an  economic  layout  of  spans, 
piers,  and  abutments  for  the  proposed  bridge,  knd  to  prepare  an  estimate 
of  cost  of  the  finished  structure,  exclusive  of  the  earth  embankments. 

Problem  B 

Given  the  profile  for  a  dry-gulch  crossing,  as  shown  in  Fig.  176,  to 
determine,  for  a  combined  highway-and-electric-railway,  reinforced-con- 
crete  arch  bridge,  having  a  clear  roadway  of  forty-four  (44)  feet  and  two 
sidewalks  each  eight  (8)  feet  wide  in  the  clear,  the  quantities  of  all  the 
materials  in  tho  structure  and  an  estimate  of  its  cost  excluding  the  earth 
fills. 

The  live  loads  ai'(!  to  l)c  taken  as  follows: 
For  the  electric  railway,  Class  25. 
For  the  wagonways,  Class  B 
For  the  sidewalks.  Class  C. 

Permissible  pressures  on  foundations,  five  and  a  half  (5.5)  tons  per  square 
foot. 

Arches  ai'c  (o  he  of  I  lie  lihbcd  tyi)e  witli  two  (2)  liiu^s  of  ribs. 

Av(!rag(^  d(^pth  of  excavation  for  foundations  is  to  be  six  (())  feet. 

For  unit  prices  of  materials  in  place,  the  average  costs  given  in  Tables 


riq  /7<f 
.  Profiles  lor  Student  Problems. 


To  face  page  14i 


TIME    AND    MONEY    IN    MAKING    COST-ESTIMATES    FOR    BRIDGES       149 

57a  and  57rf  of  "Bridge  Engineering"  are  to  be   employed,  except  that 
the  cost  for  concrete  in  arch  ribs  is  to  be  taken  as  $17.00  per  cubic  yard. 

Problem  C 

Given  the  profile  for  a  crossing,  as  shown  in  Fig.  17c,  to  determine  the 
economic  la3'-oiit  and  the  total  weight  of  structural  steel  required  for  a 
double-track,  steam-railway  trestle  to  carry  Class  55  live  load. 

Problem  D 

Given  the  profile  for  a  crossing,  as  shown  in  Fig.  17d,  to  determine  the 
economic  span-lengths  and  to  prepare  a  complete  estimate  of  cost  for  a 
reinforced-concrete-girdcr  structure  to  carry  a  thirty-six  (36)  foot  roadway 
and  two  (2)  sidewalks  each  six  (6)  feet  wide  in  the  clear,  the  roadway  being 
paved  with  creosoted-wood  blocks.  An  earth  fill  is  to  be  used  at  each  end, 
but  the  toes  of  the  front  slopes  are  not  to  extend  beyond  the  points  marked 
A  and  B  on  the  profile.  Abutments  will  not  be  employed,  the  end  columns 
being  buried  completely  in  the  embankments.  The  hve  loads  are  to  be 
Class  A  for  the  roadway  and  Class  B  for  the  sidewalks.  The  permissible 
pressure  on  the  foundations  is  to  be  three  (3)  tons  per  square  foot.  The 
depths  of  the  footings  below  ground  are  to  average  six  (6)  feet. 

The  slopes  for  the  fills  are  to  be  one  and  a  half  (1.5)  horizontal  to  one 
vertical. 

For  unit  prices  of  materials  in  place,  the  average  costs  given  in  Tables 
57a  and  57d  of  "  Bridge  Engineering  "  are  to  be  employed. 


These  four  problems  were  specially  chosen  for  the  purpose  of  making 
the  competitors  proficient  in  the  quick  computation  of  approximate 
quantities  of  materials  and  costs  of  structures,  and  to  train  their  judgment 
in  the  important  matter  of  the  determination  of  best  possible  layouts  for 
bridges. 


CHAPTER  XVIII      , 

ECONOMIC    SPAN-LENGTHS    FOR    SIMPLE-TRUSS  BRIDGES    ON    VARIOUS  TYPES 

OF    FOUNDATION 

Under  the  caption  of  this  chapter  there  was  dehvered  by  the  author 
on  September  15,  1919,  before  the  Western  Society  of  Engineers  a  paper 
based  upon  some  two  hundred  bona  fide  special  estimates  of  cost  and  illus- 
trated by  thirty-six  diagrams.  These  illustrations  are  interesting  in  that 
they  show  graphically  how  the  economics  for  various  types  of  structure 
vary  with  the  depth  of  the  foundation;  but  it  has  not  been  thought  neces- 
sary to  reproduce  here  more  than  a  single  set  (four)  of  them  and  one  addi- 
tional diagram  (Fig.  18/i)  in  which  all  the  results  have  been  combined  in 
a  general  way  by  ignoring  certain  small,  abnormal  variations  caused  by 
slight  ^regularities  due  to  the  employment  of  special  uistead  of  general 
data  in  making  the  calculations. 

The  paper  reads  as  follows: 

Up  to  the  present  time  the  general  knowledge  possessed  by  the  engineer- 
ing profession  concerning  economic  span  lengths  for  bridges  has  been  rather 
crude  and  unsatisfactory.  Until  three  decades  ago  the  only  data  available 
on  this  subject  were  covered  by  the  broad  statement  that  the  greatest 
economy  in  a  bridge  layout  exists  when  the  cost  of  a  span  is  equal  to  the 
cost  of  a  pier.  In  his  pamphlet  on  "General  Specifications  for  Highway 
Bridges  of  Iron  and  Steel,"  issued  in  1888,  the  author  pointed  out  the  fact 
that  the  then  popular  impression  concerning  this  question  was  incorrect, 
because  the  cost  of  the  floor  is  constant,  and  hence  the  adjustment  is  one 
between  cost  of  substructure  and  cost  of  metal  in  trusses  and  laterals : 
Three  years  later  he  gave,  in  a  paper  pubhshed  by  "Indian  Engineering," 
a  mathematical  demonstration  of  the  theory  of  the  economics  of  bridge 
layouts,  showing  that  the  greatest  economy  will  exist  when  the  cost  of  a 
pier  is  equal  to  one-half  of  that  of  the  trusses  and  laterals  of  the  two  spans 
which  it  helps  to  support.  This  demonstration  was  based  upon  the  assump- 
tions that  the  piers  rest  on  hard  material  at  moderate  depth  and  that,  in 
most  cases  being  of  minimum  size,  they  would  not  vary  in  dimensions  or 
total  cost  for  small  changes  in  the  span-lengths. 

This  pi'inciplc,  though,  is  not  applicable  to  the  case  of  piers  resting  on 
sand  or  on  piles,  because  the  cost  per  lineal  foot  for  substructure  is  often 
nearly  constant  for  all  moderate  span-lengths,  while  that  for  the  super- 
structures augments;  and  this  fact  is  not  at  all  generally  recognized  by 
bridge  designers.     It  has  become  evident  of  late  to  the  author  by  reason  of 

150 


ECONOMIC    SPAN-LENGTHS   FOR   SIMPLE-TRUSS   BRIDGES         151  , 

some  important  bridge  studies  which  he  has  been  called  upon  to  make  in 
his  practice,  that  there  is  needed  by  the  profession  a  systematic  investiga- 
tion to  determine  in  an  authentic  manner  the  economic  span-lengths  for 
simple-truss  bridges  to  support  the  different  kinds  of  live  loads  by  piers 
resting  on  various  types  of  foundation  at  all  practicable  depths,  and  to 
conform  to  changing  market-prices  for  materials  in  place. 

In  connection  with  the  series  of  economic  studies  on  bridge  design  which 
the  author  has  been  making,  especially  of  late  years,  and  which  he  hopes  to 
complete  before  he  passes  on,  this  question  had  to  be  settled  sooner  or 
later,  consequently  he  has  just  spent  three  weeks  in  computing  the  actual 
costs  of  both  substructure  and  superstructure  for  over  two  hundred  cases 
of  bridge  layouts  covering  the  following  combinations: 

Railway,  Highway,  and  Combined-Railway-and-Highway  Bridges  on 
Concrete  Pier-Shafts  overlying  Caissons  or  Cribs  resting  on  Sand,  Bed 
Rock,  or  Piles,  and  reaching  to  depths  below  low  water  of  50,  100,  150,  200, 
and  250  feet;  also  for  low,  medium,  and  high  conditions  of  the  material 
market. 

The  fact  that  all  the  computations  were  prepared  by  the  author  alone, 
and  without  a  detailed  check  on  the  figuring,  need  not  cause  any  doubt 
about  the  correctness  of  the  results  of  his  work,  because  all  of  them  were 
plotted  on  cross-section  diagrams,  and,  consequently,  whenever  any  error 
of  the  least  importance  was  made  it  was  detected  at  once. 

This  investigation  owes  its  existence  to  the  fact  that  recently  the  author 
as  a  member  of  the  Board  of  Advisory  Engineers  to  the  Public  Belt  Railroad 
Commission  of  New  Orleans  (appointed  to  study  the  question  of  bridging 
or  tunneling  the  Mississippi  River  at  or  near  that  city),  had  occasion  to 
make  a  large  number  of  layouts  with  cost  estimates  for  railway,  highway, 
and  combined-railway-and-highway  bridges  having  sand  foundations  two 
hundred  and  fifty  feet  below  the  Gulf  level.  While  the  conditions  prece- 
dent for  those  computations  were  used  for  certain  of  the  layouts  of  this 
investigation,  the  actual  results  thereof  were  not  incorporated,  because  all 
the  calculations  involved  in  this  paper  were  special  and  had  to  be  systema- 
tized. However,  there  were  numerous  deductions  made  from  the  New 
Orleans  Bridge  studies,  which  permitted  the  adoption  of  valuable  short 
cuts  in  figuring. 

A  large  portion  of  the  data  employed  in  making  estimates  of  cost  was 
taken  from  the  various  diagrams  given  in  "Bridge  Engineering,"  including 
live  loads,  impact,  and  weights  of  metal. 

The  following  are  the  assumptions  and  conditions  precedent  adopted 
for  the  series  of  calculations: 

Character  of  Structures 

The  different  classes  of  bridges  covered  are  Double-Track-Railway, 
Single-Track-Railway,  Standard-Highway,  and  Combined  Double-Track- 


152  ECONOMICS   OF   BRIDGEWORK  Chapter  XVIII 

Railway-and-Highway,  all  metal  being  carbon  steel  (excepting  in  one  set 
of  estimates  where  nickel  steel  was  employed),  the  railway  floors  bemg 
open,  the  highway  floors  being  paved  with  creosoted  blocks  resting  on  a 
reinforced-concrete  base,  the  foot-walks  being  slabs  of  reinforced  grani- 
toid, and  the  handrails  being  of  steel. 

The  highway  bridges  considered  are  all  of  the  author's  adopted  standard 
type,  viz.,  carbon-steel  trusses,  laterals,  and  floor-system  with  a  42-foot 
paved  roadway  supported  on  a  reinforced-concrete  base,  two  8-foot  side- 
walks of  reinforced  granitoid  carried  on  cantilever  brackets,  and  two  steel 
handrails,  making  the  deck  about  sixty  feet  wide  from  out  to  out,  exclusive 
of  the  space  occupied  by  the  trusses  in  through  bridges. 

All  pier-shafts  are  of  plain  concrete  with  a  coping,  the  batter  being 
1"  to  1'  for  low-level-railway  and  low-level-combined  bridges,  f'to  V 
for  high-level-railway  and  high-level-combined  bridges,  and  ^"  to  1'  for 
highway  bridges. 

All  caissons  founded  on  sand  are  of  timber  with  concrete  filling  and 
having  steel  bases  and  cutting  edges;  and  they  are  made  as  hght  as  is 
legitimate  by  omitting  to  fill  a  large  proportion  of  the  excavating  shafts. 
But  when  the  caissons  reach  bed  rock  they  are  assumed  to  be  filled  solid. 
The  depth  of  water  in  each  case  is  taken  as  one-third  of  the  vertical  dis- 
tance between  extreme  low  water  and  caisson  footing. 

In  the  pile  piers  the  piles  are  seventy-five  feet  long  and  project  sixty 
feet  below  the  bases,  which  are  assumed  to  be  twenty  feet  high,  the  piles 
being  spaced  three  feet  from  center  to  center. 

The  character  of  the  materials  passed  through  during  the  sinking  is 
assumed  to  be  the  ordinary  mixture  of  silt,  quicksand,  soft  gumbo,  and 
other  river  deposits,  overlying  either  coarse  sand  suitable  for  foundations, 
or  bed  rock. 


Methods  of  Pier  Sinking 

The  methods  assumed  for  sinking  the  caissons  are  those  of  open  dredg- 
ing and  the  pneumatic  process,  the  former  being  employed  when  the  bases 
are  to  rest  on  sand  and  the  latter  when  they  are  to  reach  bed-rock.  In  the 
case  of  pile  piers,  the  open  box  is  first  to  he  sunk  by  dredging  to  the  required 
depth,  then  the  piles  are  to  be  driven  inside  of  it,  and  finally  the  remaining 
space  is  to  be  filled  with  concrete. 

RPECTFICATIONS    FOR    DESIGNING 

The  specifications  for  the  designing  of  suixMstmcture  are  those  given  in 
r^hai)t(!r  LXXVIII  of  "Bridge  Engineering,"  and  those  for  the  designing  of 
subsl  lucture  arc  to  be  found  in  (chapters  XXXIX  to  XLlll,  inclusive,  of 

that   treatise. 


ECONOMIC    SPAN-LENGTHS    FOR    SIMPLE-TRUSS    BRIDGES 


153 


Loads 

The  live  loads  for  superstructure  for  the  several  kinds  of  bridges  are 
given  on  Fig.  18a,  and  those  for  substructure  on  Fig.  186.  The  former 
include  impact  allowances,  while  the  latter  do  not.     Fig.  18c  records  the 


300 


AOO 


500  ^tOSS^Zt.  &  ES3ER    SSP<^W  YORK.    NodOQ. 

5pan     in  Feeh 

Fig.  18a.     Live-Plus-Impact  Loads. 

weights  of  metal  per  lineal  foot  of  span  in  the  superstructures  of  the 
various  kinds  of  bridges  considered.  The  live  loads  for  highway  and  com- 
bined-railway-and-highway  bridges  include  the  proper  aUowances  for 
electric-railway  cars  or  trains. 

The  weights  per  lineal  foot  for  the  flooring  are  as  given  in  Table  18a. 


154 


ECONOMICS    OF   BEIDGEWORK 


Chapter  XVIII 


Permissible  Pressures  on  Soil  and  Piles 
For  sand   foundations   the   method   of   determining   the   permissible 
pressure  beneath  the  base  of  the  caisson  is  that  evolved  by  the  author  in 
making  his  before  mentioned  computations  for  the  New  Orleans  Bridge 


C 
0- 

:5 


> 

-3 


l5 


iZoooii 


400 


Lodded   Lengrh  in  Fcah 

Fig.  186.     Live  Loads  Without  Impact. 

study.  It  consists  of  allowing  four  tons  per  square  foot  plus  the  intensity 
of  i)rcssurc  on  the  adjacent  soil  at  the  elevation  of  the  base,  due  to  thewe^ 
weight  of  the  overlying  solid  material,  after  having  deducted  from  the  net 
weight  of  the  caisson  and  its  superimposed  load  for  side  friction  at  the  rate  of 
400  pounds  per  square  foot  of  lateral  sinfacc  in  contact  with  solid  material. 
The  not  weight  of  the  water-soaked  timber  in  the  caisson  is  taken  as  zero 


ECONOMIC   SPAN-LENGTHS   FOR   SIMPLE-TRUSS   BRIDGES 


155 


and  that  of  the  concrete  at  eighty  pounds  per  cubic  foot.     The  partially-filled 
caissons  when  complete  weigh  about  fifty-six  pounds  net  per  cubic  foot. 

As  a  matter  of  precaution,  the  caissons  have  to  be  figured  for  side- 
frictional  resistance  of  600  pounds  per  square  foot  during  sinking,  or  some- 


o       ^oo     200    200     Aoo     SCO     aoa^EL  rroiSeR  SOQcw^ioaf.  no)qobi. 
Sp<3n      '\n   Feef- 

FiG.  18c.    Total  Weights  of  Metal  in  Superstructures. 

times  (in  extreme  cases)  500  pounds  per  square  foot.  Of  course,  it  is  prac- 
ticable to  load  temporarily  the  caisson  as  it  reaches  the  neighborhood  of  its 
final  position;  but  such  an  expedient  is  sometimes  costly  and  troublesome, 
hence  it  is  better  to  design  it  large  enough  to  avoid  the  probabihty  of  holdup. 
Some  engineers  have  objected  to  relying  upon  side  friction  in  supporting 
the  load,  but  their  contention  is  wrong,  because  it  certainly  does  exist, 
and  it  has  to  be  overcome  before  any  settlement  of  the  finished  pier  can 


156 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XVIII 


occur.  In  the  case  of  long  piles  driven  into  soft  material,  it  is  almost 
entirely  the  side  friction  which  gives  them  supporting  power.  Again, 
someone  may  question  the  correctness  of  loading  sand  apparently  as  high 
as  nine  tons  per  square  foot  at  a  depth  of  250  feet  below  low  water  level, 
when  the  depth  of  water  is  eighty  feet;  but  it  must  be  remembered  that  the 
net  weight  of  170  feet  of  earth  loads  the  soil  some  five  tons  per  square  foot, 
and  that  before  any  settlement  can  occur,  the  material  adjacent  to  the 
caisson  has  to  be  raised.  The  reason  for  this  is  that  the  sand  at  such  a 
great  depth  is  practically  incompressible,  so  that  for  any  settlement  to 
occur  it  must  flow.  It  cannot  flow  downward  or  laterally,  because  there  is 
no  vacant  space  for  it  to  fill;  consequently,  if  flow  it  must,  it  will  have  to 
pass  upward;  and,  in  order  to  do  so,  it  must  lift  a  large  column  of  the  adja- 
cent solid  material.  In  the  author's  opinion,  it  would  take  an  excessively 
large  unit  loading  on  the  base  of  a  filled  caisson  resting  on  coarse  sand  at  a 
depth  of  two  hundred  and  fifty  feet  to  cause  the  slightest  settlement. 

TABLE    18a 


Character  of  structure 

Weight  per  Lineal  Foot 
for  Flooring  Exclusive  of  all 
Steel  but  Reinforcing  Bars 

Low  level  combined  bridges 

5,800  pounds 

High  level  combined  bridges 

6,900  pounds 

Double-track-railway  bridges              

900  pounds 

Single-track-railway  bridges.         

450  pounds 

Standard  highway  bridges 

6,100  pounds 

The  permissible  loading  for  long  piles  has  been  taken  at  forty  tons  per  pile, 
this  being  in  accordance  with  the  author's  practice  for  a  quarter  of  a  century ; 
and  he  has  never  yet  found  any  settlement  to  occur  under  such  loading. 

Unit  Prices  of  Materials  in  Place 
The  following  table  gives  the  unit  prices  for  materials  in  place  assumed 
for  the  purpose  of  this  investigation: 

TABLE   186 


Materials 


Structural  steel,  per  pound 

Concrete  shafts  of  20'  average  thickness,  per 

cubic  yard 

Mass  of  caissons,  including  all  materials,  for  a 

width  of  30'  and  a  height  of  150',  sunk  by 

open-dredging,  per  cubic  yard 

Mass  of  cribs,  including  enclosed  pile-heads, 

per  cubic  yard 

Portion  of  long  piles  projecting  below  base  of 

crib,  per  lineal  fool 


Condition  of  Market 


Low 


4p 
$9.00 

15.00 
15.00 

.75 


Medium 


6^ 
$12.00 

20.00 

20.00 

1.00 


High 


|;i5.oo 

25.00 

25 .  00 

1.25 


ECONOMIC    SPAN-LENGTHS    FOE    SIMPLE-TEUSS   BEIDGES         157 

For  the  "Medium  Condition  of  Market/'  the  price  per  cubic  yard  of  the 
shafts  is  to  be  modified  by  the  addition  or  subtraction  of  fifteen  cents  for 
each  foot  of  variation  from  the  assumed  average  of  twenty,  the  greater  the 
thickness  the  smaller  the  unit  price.  For  instance,  if  a  shaft  were  12  feet 
wide  under  coping  and  18  feet  wide  at  the  bottom,  the  average  width  would 
be  15  feet  and  the  unit  price  for  medium  market  $12.75. 

For  the  same  market  condition  the  unit  price  for  mass  of  caissons  is  to 
be  modified  by  the  addition  or  subtraction  of  ten  cents  for  each  foot  of 
variation  from  the  assumed  average  of  thirty,  the  wider  the  caisson  the 
smaller  the  price  per  cubic  yard.  Again,  for  the  said  market  condition,  the 
unit  price  for  mass  of  caissons  is  to  be  modified  by  the  addition  or  sub- 
traction of  two  cents  for  each  foot  of  variation  from  the  assumed  average 
height  of  one  hundred  and  fifty  feet,  the  deeper  the  caisson  the  smaller  the 
unit  price.  For  instance,  with  medium  condition  of  market,  the  unit  price 
for  a  caisson  twenty-six  feet  wide  and  two  hundred  and  forty  feet  high 
would  be 

20.00+4X0.10-90X0.02  =  $18.60. 

For  the  other  two  assumed  conditions  of  the  market,  these  figures  of 
modification  would  have  to  be  multiplied  by  the  ratios  indicated  in  the 
table,  viz.,  0.75  and  1.25. 

Without  these  modifications  of  unit  prices  for  substructure,  the  investi- 
gation would  be  not  only  illogical,  but  incorrect.  The  variation  in  cost  of 
shafts  per  cubic  yard  is  due  primarily  to  the  lower  unit  cost  of  forms  for 
thick  piers,  but  also  somewhat  to  the  economy  effected  by  manufacturing 
and  handling  larger  masses  of  concrete.  The  latter  reason  applies  also  to 
the  two  variations  in  the  cost  of  mass  of  caissons;  but  the  main  cause  there- 
of is  that  the  total  cost  of  cutting  edge,  shelter  against  current,  and  flota- 
tion to  final  location  are  the  same  for  a  shallow  base  as  for  a  deep  one. 

The  prices  per  cubic  yard  for  caissons  sunk  by  the  pneumatic  process, 
under  medium-market  conditions,  have  been  made  two  dollars  greater  than 
those  for  caissons  sunk  by  open-dredging.  This  is  in  conformity  with  the 
author's  bridge  experience  of  nearly  four  decades.  It  is  due  primarily  to 
the  more  rapid  sinking  by  open  dredging  and  the  greater  cost  of  the  pneu- 
matic outfit,  but  also  to  the  fact  that  the  pneumatic  caissons  are  generally 
filled  solid,  while  the  open-dredging  caissons  often  have  their  excavating 
wells  only  partially  filled. 

,  The  price  used  for  nickel  steel  superstructure  in  place  for  medium 
market  conditions  has  been  taken  as  eight  and  a  half  cents  per  pound;  for 
the  reason  that  the  last  ante-bellum  figures  quoted  to  the  author  made 
:the  price  of  nickel-steel  two  and  a  half  cents  per  pound  higher  than  that  of 
(B^rbon-steeL  The  weights  of  metal  in  nickel-steel  superstructures  were 
qojnjpujbed  by  means  of  ratios  determined  from  diagrams  given  in  the 
a^tlvor's-. paper  "Nickel  Steel  for  Bridges."* 

-ryi'y  '3/;.-  -M  *  See  Trans.  Am.  Soc.  Civ.  Engrs.  for  1909. 


158  ECONOMICS   OF  BRIDGEWORK  Chapter  XVIII 

Method  of  Determining  the  Economic  Span-Lengths 

In  determining  the  economic  span-lengths,  computations  were  made 
for  the  volumes  of  concrete  in  shafts,  volumes  of  caissons,  volumes  of  cribs, 
total  lengths  of  piles  below  crib  bases,  and  weights  of  metal  in  spans,  but  no 
notice  was  taken  of  the  cost  of  flooring,  as  that  is  a  constant  for  any  type  of 
bridge. 

It  might  be  well  to  mention  that  while  the  abscissae  of  the  diagrams  give 
the  span  lengths  measured  from  center  to  center  of  end  pins,  the  costs  of 
structure  per  lineal  foot  were  computed  by  using  the  distance  from  center 
to  center  of  piers. 

In  making  each  of  these  cost  estimates  there  was  assumed  a  structure  of 
indefinitely  great  length  and  unvarying  profile,  so  that  the  sum  of  the  cost 
of  the  steel  work  in  a  span  and  the  cost  of  a  complete  pier  divided  by  the 
horizontal  distance  between  adjacent-pier  centers  gives  the  comparing  cost 
per  lineal  foot  of  structure,  although,  as  before  indicated,  not  the  complete 
cost  thereof. 

The  results  of  all  calculations  made  were  plotted  on  cross-section  dia- 
grams, but  only  a  few  thereof  have  been  reproduced  herein.  However,  the 
important  deductions  from  all  the  estnuates  hav^e  been  tabulated.  The 
plotting  was  done  with  the  utmost  care,  and  due  consideration  was  given  to 
a  proper  determination  of  the  economic  span-length.  As  previously  indi- 
cated, a  number  of  arithmetical  errors  were  located  and  corrected  by  reason 
of  irregularities  in  the  curves,  thus  maldng  the  latter  truly  reliable.  In 
almost  all  cases,  at  least  four  points  were  plotted  from  computations,  in 
order  to  locate  the  curves  of  cost  for  substructure  and  for  the  steelwork  of 
superstructure;  and  a  combination  of  these  was  used  for  locating  a  few 
intermediate  points  on  the  curve  which  gives  the  combined  cost  of  sub- 
structure and  steelwork.  In  a  few  instances,  though,  three  points  for  the 
lower  curves  were  found  to  be  sufficient  for  a  correct  plotting  of  the  upper 
curve. 

Recording  Diagrams  and  Table 

On  Figs.  IM  to  18g,  inclusive,  are  graphically  recorded  specimen  dia- 
grams of  the  results  of  the  special  calculations.  Each  diagram  contains 
three  curves,  one  for  substructure,  one  for  steelwork  in  superstructure,  and 
the  other  for  a  combination  of  these  two.  The  computed  cost  points  there- 
for are  marked  on  the  three  curves,  respectively,  by  circles,  squares,  and 
diamonds.  The  abscissse  of  these  diagrams  give  the  span-lengths  in  feet, 
measuring  from  center  to  center  of  bearings;  and  the  ordinates  record  the 
cost  per  lineal  foot,  measuring  from  center  to  center  of  piers.  On  each 
diagram  is  clearly  indicated  the  span-length  for  greatest  economy ;  and  it  is 
to  be  noticed  by  the  flatness  of  the  upper  curves  that  a  variation  of  twenty- 
five  feet  or  more,  either  aljove  or  below  the  economic  length,  will  make  very 


ECONOMIC    SPAN-LENGTHS    FOR   SIMPLE-TRUSS   BRIDGES         159 


little  difference  in  the  cost  per  foot  of  structure.  Each  diagram  is  provided 
with  a  title  which  indicates  clearly  the  type  of  structure  and  depth  of 
foundation    to  which  it  refers.     Unless  otherwise  shown   thereon,  these 


YTOOf 


200 


2S0 


450 


BX) 


300  350  400 

Spxan  in    Feef 

Fig.  ISd.     Costs  per  Lineal  Foot  of  Structure  for  Low-Level,  Combined  Bridges  on 
Sand  Foundations  100  Feet  Deep. 

diagrams    relate    to    normal    or    medium    conditions    of    the    material 
market. 

In  the  following  table  is  given  a  resume  of  the  results  of  most  of  the  cost 
computations  that  were  prepared: 


160 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XVIII 


TABLE   ISc 

Resume  of  Results  op  Computations 


Character  of  Structure 


Character 
of  Foun- 
dations 


Low-Level  Combined 

Low-Level  Combined 

Low-Level  Combined.  ... 
Low-Level  Combined .... 
Low-Level  D.  T.  R.  R. .  .  . 
Low-Level  D.  T.  R.  R.  .. 

Low-Level  D.  T.  R.  R 

Low-Level  D.  T.  R.  R.  .. 
High-Level  Combined. .  .  . 
High-Level  Combined. .  . . 
High-Level  Combined. .  .  . 
High-Level  Combined. ... 
Low-Level  Combined .... 
Low-Level  Combined .... 
Low-Level  D.  T.  R.  R. .  .  . 
Low-Level  D.  T.  R.  R.  .. 
High-Level  Combined. ... 
High-Level  Combined. .  .  . 
Low-Level  S.  T.  R.  R. .  .  . 
Low-Level  S.  T.  R.  R. .  .  . 
High-Level  Combined. .  .  . 

Low-Level  Highway 

Low-Level  Highway 

Low-Level  Highway 

Low-Level  Highway 

High-Level  Highway 

High-Level  Highway 

High-Level  Highway 

High-Level  Highway 

Low-Level  D.  T.  R.  R.  .  . 

Low-Level  D.  T.  R.  R.  .  . 

Low-Level  D.  T.  R.  R.  .  . 

Low-Level  D.  T.  R.  R.  .  . 

Low-Level  D.  T.  R.  R .  .  . 

Low-Level  D.  T.  R.  R.  .  . 

Low-Level  D.  T.  R.  R.  .  . 

Low-Level  D.  T.  R.  R.  .. 

Low-Level  D.  T.  R.  R.  .  . 

Low-Level  D.  T.  R.  R.  .. 

Low-Level  D.  T.  R.  R.. .  . 

Low-Level  D.  T.  R.  R.  .. 


Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Rock 
Rock 
Rock 
Rock 
Rock 
Rock 
Rock 
Rock 
Piles 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 
Sand 


Depth  of 
Caisson 
Footings 


100' 
150' 
200' 
250' 
100' 
150' 
200' 
250' 
100' 
150' 
200' 
250' 

50' 
100' 

50' 
100' 

50' 
100' 

50' 
100' 

20' 
100' 
150' 
200' 
250' 
100' 
150' 
200' 
2.50' 
100' 
150' 
200' 
250' 
100' 
1-50' 
200' 
250' 
100' 
150' 
200' 
250' 


Economic 

Span 
Lengths 


275' 
300' 
325' 
350' 
275' 
310' 
360' 
430' 
275' 
300' 
325' 
350' 
250' 
300' 
275' 
325' 
300' 
350' 
250' 
300' 
175' 
300' 
350' 
400' 
450' 
325' 
350' 
375' 
400' 
350' 
385' 
425' 
470' 
290' 
330' 
375' 
425' 
275' 
325' 
375' 
425' 


Remarks 


Shaft  Batter 
l"to  1' 


Shaft  Batter 
1"  to  1' 


Shaft  Batter 
f "  to  1' 

Pneumatic 

Caissons 
Pneumatic 

Caissons 
Pneumatic 

Caissons 
Pneumatic 

Caissons 
Pile  Piers 

Shaft  Batter 
¥'  to  1' 


Shaft  Batter 
¥'  to  1' 


Nickel-Steel 
Super- 
Structure 

Ijow-Market 
Unit-Prices 


High-Market 
Unit-Prices 


These  results  are  recorded  graphically  in  Fig-  18/i. 


ECONOMIC    SPAN-LENGTHS   FOR   SIMPLE-TRUSS   BRIDGES 


161 


From  a  study  of  the  preceding  table  there  can  be  drawn  the  following 
deductions : 

A.  For  all  types  of  bridges  the  economic  span-length  increases  with  the 
depth  of  foundation,  though  not  necessarily  in  the  same  proportion. 


1700 
1600 
I50C 


ZOOtriliiill 


ffiffll 


SPffi 


[Cost 


pen ;  hn.{i\c(i'5frod\Jrei 

J — 1-' —  I ' f    ^1 — I — til' — 1~ — ^ -t- 


m^mmmmm 


250 


300 


450 


500 


350  ^0 

5pan  In  Yeel 

Fig.  18e.     Costs  per  Lineal  Foot  of  Structure  for  Low-Level,  Combined  Bridges  on 
Sand  Foundations  150  Feet  Deep. 

B.  The  lighter  the  superstructure  and  the  live  load  it  carries,  the 
greater  generally  is  the  economic  span-length,  and  the  greater  the  variation 
of  the  latter  with  the  depth  of  foundation. 


162 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XVIII 


C.  For  sand  foundations  there  is  not  much  difference  in  the  economic 
span-lengths  for  low-level  and  liigh-level  bridges  of  the  same  type. 

D.  Structures  with  piers  founded  on  bed  rock  generally  have  economic 


250 


450 


500 


300  350  400 

Span  In    Feef- 

FiG.  18/.     Costs  per  Lineal  Foot  of  Structure  for  Low-Level,  Combined  Bridges  on 
Sand  Foundations  200  Feet  Deep. 

span-longths  somewhat  greater  than  tliose  of  ihc  e()i-rcs])on(Ung  structures 
founded  upon  sand  at  the  same  depth. 

E.     Single-track  railroad-biidges  have  economic  span-lengths  a  little 
less  than  those  of  the  corresponding  double-track  structures. 


ECONOMIC    SPAN-LENGTHS   FOR   SIMPLE-TRUSS    BRIDGES         163 

F.     Pile  piers  for  high-level  bridges  involve,  for  economic  considera- 
tions, rather  short  spans;  and  for  low-level  structures  they  usually  neces- 


4O0tt±t 

250 


300 


400 


450 


SCO 


350 
Span  in    Feeh 

FiG.  18^.     Costs  per  Lineal  Foot  of  Structure  for  Low-Level,  Combined  Bridges  on 
Sand  Foundations  250  Feet  Deep. 


sitate  such  short  ones  as  to  require  the  adoption  of  plate-girder  super- 
structures. 

G.     In  highway  bridges  having  very  deep  foundations  on  sand,  increas- 
ing the  batter  of  the  shaft  augments  the  economic  span-length. 


164 


ECONOMICS    OF    BRIDGEWORK 


Chapter  XVIII 


H.  Using  nickel  steel  instead  of  carbon  steel  in  the  superstructure 
increases  materially  the  economic  span-length. 

I.  The  assumed  variations  in  unit  prices  with  changing  market  condi- 
tions make  very  httle  difference  in  the  economic  span-lengths.  There 
would  have  been  no  difference  at  all  had  the  prices  of  all  the  materials  used 
been  assumed  to  vary  in  the  same  proportion ;  but  the  superstructure  steel, 


60 


220       240 


Fig.  18/i. 


80  m         120         MO        160         180        200 

Depfh  of  rou/jdafion  be/s^-  low  Wafer  le\/el  in  Feef 

Economic   .SiJan-Lcngths   for   Siinplc-Truss   Bridges   on   Various   TyiJe'S   of 
Foundation. 


erected,  ordinarily  changes  in  value  somewhat  more  rapidly  than  docs  the 
substructure  of  the  ])ri(lge. 

J.  There  arc  not  many  irregularities  to  be  found  in  comparing  the 
diagrams  or  the  tal)ulatc(l  results  of  the  calculations;  and  what  few  exist 
arc  small.  They  arc  generally  due  to  the  adoption  of  a  mininuun  weight 
limit  for  sinking  to  grcuit  depths  instead  of  figuring  upon  employing  tem- 
porary  loading. 

Certain  of  tlio  cost  curves  in  fh(>  dingi-anis,  in  combination  with  oIIum- 
diagrams  giving  weights  of  steel  (list  ril)ut('(l  Ix-lwccn  trusses,  laterals,  and 


ECONOMIC    SPAN-LENGTHS    FOR    SIMPLE-TKUSS    BlilDCES         166 

floor  systems,  will  provide  a  check  on  the  correctness  of  the  old  method  of 
determining  economic  span-lengths.  Let  us  take  the  case  of  a  low-level, 
double-track-railway  bridge  founded  on  rock,  find  the  cost  per  lineal  foot 
of  the  trusses  and  laterals  in  the  span  of  economic  length,  and  check  it 
against  the  cost  per  lineal  foot  for  the  substructure  thereof.  For  a  50-foot 
depth  of  bed  rock  the  economic  span-length  is  275  feet;  and  for  that  span 
(see  "Bridge  Engineering,"  pages  1239  and  1240)  the  weight  of  metal  per 
lineal  foot  for  trusses  and  laterals  with  Class  60  live  load  is  4,600  pounds, 
which  at  six  cents  per  pound  would  be  worth  $276,  while  the  cost  per  foot 
for  the  substructure  given  by  the  diagram  is  $270.     This  is  not  a  bad  check. 

For  a  depth  of  100  feet,  the  economic  span-length  is  325  feet,  for  which 
the  weight  of  trusses  and  laterals  is  5,860  pounds,  which  at  six  cents  per 
pound  would  be  worth  $352.  The  diagram  makes  the  cost  per  foot  for  the 
substructure  $420 — quite  a  discrepancy. 

For  low-level,  single-track-railroad  bridges  with  a  foundation  depth  of 
50  feet,  the  economic  span-length  given  by  diagram  is  250  feet,  for  which 
the  weight  of  trusses  and  laterals  is  2,480  pounds,  which  at  six  cents  per 
pound  would  be  worth  $149,  while  the  said  diagram  gives  the  cost  per  foot 
for  substructure  at  $175 — not  a  close  check. 

For  a  depth  of  100  feet,  the  economic  span-length  is  300  feet,  for  which 
the  weight  of  trusses  and  laterals  is  3,050  pounds,  which  at  six  cents  per 
pound  would  be  worth  $183.  The  diagram  makes  the  cost  per  foot  for 
substructure  $275 — another  large  variation. 

It  is  evident  from  the  preceding  comparisons  of  cost  that  the  former 
rule  for  determining  the  economic  span-length  is  not  reliable,  especially 
for  foundations  at  great  depths;  hence  its  use  should  be  discontinued. 

There  is  a  little  economic,  or  more  strictly  speaking  uneconomic,  investi- 
gation concerning  simple-truss  spans  the  results  of  which  are  worth  know- 
ing and  may  sometimes, prove  valuable,  especially  in  answering  questions 
propounded  by  laymen,  viz.,  "what  are  the  relative  weights  of  metal  in 
equal- truss,  three-span  bridges  and  structures  of  the  same  kind,  same 
total  length,  and  same  loading,  but  having  the  central  span  lengthened  and 
the  other  two  equally  shortened?  "  The  answer  to  this  question  is  that  the 
weight-ratios  for  the  unequal-span  layouts,  as  compared  with  those  for 
equal  spans,  are  greater  for  long  structures  than  for  short  ones,  and  increase 
with  the  ratio  of  middle-span  length  to  average-span  length.  The  values 
of  such  ratios  for  three-span  structures,  varying  in  average  span-length  by 
one  hundred  feet  from  200  feet  to  500  feet,  are  given  in  Fig.  18i. 

The  curves  for  cost  ratios  are  almost  coincident  with  those  for  w^eight- 
ratios,  because  the  pound  prices  erected  for  the  metal  in  the  various  lay- 
outs are  nearly  alike.  On  the  one  hand,  those  for  the  equal-span  layouts 
should  be  less  because  of  a  saving  in  cost  of  making  working  drawings  and 
templets;  but,  on  the  other  hand,  the  erection  costs  per  pound  are  a  trifle 
less  for  the  layouts  of  unequal-span  length  because  of  their  greater  total 
weights  of  metal.     C.  W,  Bryan,  Esq.,  Chief  Engineer  of  the  American 


166 


ECONOMICS    OF   BRIDGEWORK 


Chapter  XVIII 


Bridge  Company,  has  ver}"  kindly  investigated  this  question  for  the  author; 
and  in  a  letter  dated  January  29th,  1920,  he  reports  as  follows  concerning  a 
double-track,  steam-railway  bridge,  1,200  feet  long,  for  which  the  metal 
erected  is  assumed  to  cost  1  .^i  per  lb.: 

After  careful  study  I  feel  that  the  three  equal  spans  and  the  two  spans  of  350  feet 
with  one  of  500  feet  should  take  the  same  pound  price.     For  the  two  spans  of  300  feet 


//        7 J        14         15        /.6         1.7        1.8         1.9 
J^af/os  of  Len^f/)  ofAf/dd/e  Span  fo  fhahf  (fi^era(je  Jpan 

Fig.  18i.     Diagram  of  Weight-Ratios  showing  Effect  of  Lengthening  the  Central  Span 
of  any  Simple-Truss,  Three-Span  Layout,  Keeping  the  Total  Length  Unchanged. 

and  one  of  600  feet  I  would  reduce  the  price  $1.00  per  ton  or  to  6.95^5  per  pound;  and 
for  the  two  250-foot  spans  and  one  700-foot  span,  I  would  reduce  the  price  $2.00  per 
ton,  or  to  6.90c.  per  pound. 

As  the  extreme  variation  in  pound  price  is  only  one-and-a-half  per  cent, 
evidently,  as  before  stated,  it  is  not  worth  while  tt)  make  a  special  diagram 
recording  total  cost-ratios  for  uneconomic,  three-span,  simple-truss  lay- 
outs; because  those  for  the  weight-ratios  thereof  will  suffice. 


CHAPTER  XIX 


ECONOMICS    OF    SUBSTRUCTURES 


In  the  old  days  of  cut-stone-masonry  piers,  the  method  of  proportion- 
ing the  shafts  was  to  make  them  as  small  as  possible  on  top,  keeping  the 
pedestals  of  the  spans  just  within  the  periphery  hmits  of  the  first  sub-coping 
course,  putting  on  a  batter  of  half  an  inch  to  the  foot,  and  carrying  this 
down  as  low  as  the  governing  conditions  would  permit,  thus  ignoring 
entirely  the  effect  of  thrust  from  trains  or  wind.  For  the  small  structures 
of  those  times,  with  their  short  spans,  this  arrangement  generally  answered 
the  purpose  well  enough,  because  the  maximum  theoretical  thrusts  assumed 
in  modern  bridge  practice  seldom,  if  ever,  came  upon  the  structures;  but 
occasionally  there  would  arise  a  case  for  which  this  rule-of-thumb  method 
of  pier-shaft  proportioning  would  not  suffice. 

The  author  recalls  an  experience  of  the  late  eighties  when  at  Albuquer- 
que, New  Mexico,  he  was  making  the  preliminary  calculations  for  the  Red 
Rock  cantilever  bridge  over  the  Colorado  River.  The  Chief  Engineer  of 
the  railroad  company  had  undertaken  the  designing  of  the  piers,  and  after 
learning  the  area  required  for  the  main  pedestals,  he  proportioned  the 
coping,  then  laid  out  the  rest  of  the  shaft  with  a  batter  of  one-half  inch  to 
the  foot,  and  submitted  the  design  to  the  author  for  comment.  A  glance 
brought  the  instant  conclusion  that  something  was  wrong,  and  upon  this 
being  stated  the  job  of  pier-designing  was  turned  over  to  him,  whereupon 
he  proceeded  to  figure  the  overturning  effect  on  the  pier  by  combined  trac- 
tion and  wind  loads,  with  the  result  that  a  batter  of  one  and  a  quarter 
inches  to  the  foot  was  found  necessary;  and  this  batter  gave  the  layout  a 
decidedly-pleasing  appearance. 

The  day  of  cut-stone-masonry  piers  is  past — or,  at  any  rate,  ought  to  be; 
for  compared  with  concrete  piers  they  are  always  uneconomical.  Some- 
times, as  a  defence  against  the  grinding  effect  of  ice,  or  the  disintegrating 
effects  of  sea-water  between  high-water  and  low-water  levels,  it  is  necessary 
to  protect  the  concrete  thus  exposed  with  a  facing  of  granite  or  other  hard 
rock;  and  occasionally  someone  desires  to  adhere  to  cut-stone  work  for 
the  sake  of  retaining  the  old-fashioned  appearance  which  it  gives  to  struc- 
tures; but  no  engineer  who  is  a  student  of  true  economy  in  design  and  con- 
struction will  continue  to  use  coursed  masonry  in  his  bridge  piers. 

There  is  an  economic  problem  in  concrete-pier  designing  which  comes  up 
occasionally — whether  it  is  better  to  reinforce  for  bending  due  to  traction 
and  wind  loads  or  to  omit  the  rods  and  use  more  concrete.     There  is  no 

167 


168  ECONOMICS   OF   BRIDGEWORK  Chapter  XIX 

means  of  settling  this  except  to  design  the  shaft  in  both  ways  and  com- 
pute the  costs.  Even  then  it  may  not  be  economics  but  aesthetics  which 
will  govern  the  decision,  because  the  reinforced-concrete  piers  are  liable  to 
lack  the  massive  appearance  which  is  necessary  for  a  pleasing  effect.  Un- 
less there  be  some  really-material  advantage  in  reinforcing  the  shafts,  it  is 
generally  better  to  build  them  of  plain  concrete. 

There  is  an  economic  expedient  in  pier  designing  that  is  very  often 
perfectly  legitimate,  especially  in  small  structures  and  occasionally  in  very 
large  ones,  viz.,  the  use  of  the  "dumb-bell"  cross-section,  or,  in  other  words, 
adopting  two  pedestals  with  a  diaphragm  wall  betv/een.  This  wall  may 
either  rest  on  a  continuous  base  or  may  be  entirely  unsupported  between  the 
pedestal  bases,  thus  acting  as  both  a  strut  and  a  beam.  The  appearance  of 
a  structure  having  piers  of  this  type  is  not  unpleasing,  and  the  effect  of 
massiveness  is  obtained  by  the  expenditure  of  very  little  extra  material. 
In  a  wide,  two-truss  bridge,  solitary  pedestals  without  a  connecting  wall 
may  be  employed,  reliance  being  placed  upon  the  end  floor-beams  of  the 
spans  to  divide  the  wind  load  about  equally  between  the  two  supports. 
In  case  that  the  deck  is  fairly  close  to  the  water,  the  great  width  will  par- 
tially hide  the  substructure,  and  the  lack  of  the  connecting  wall  will  not  be 
noticed ;  but  in  a  high-level  bridge,  especially  when  carrying  railroad  trains, 
pedestal  shafts  not  only  produce  a  flimsy  appearance  but  also  fail  to  resist 
properly  the  rack  from  the  live  load.  The  Missouri  River  bridge  at  Glas- 
gow was  originally  built  in  that  manner;  and  the  experience  with  its  piers 
was  so  unsatisfactory  that  the  twin  pedestals  had  to  be  remoued.  and 
replaced  by  a  solid  shaft.  '.     ■ 

In  some  cases  it"  is  essential  that  the  load  on  the  foundations  be  reduced 
to  an  absolute  minimum,  and  to  this  end  hollow  shafts,  or  pedestals'  con- 
nected by  two  thin  walls,  may  be  employed;  and  the  excavating  shafts  in 
the  bases  need'  not  be  filled,  excepting  only  sufficiently  at  the  bottom  to 
transfer  properly  the  upward  thrust  of  the  foundation  into  the  solid  por- 
tions of  the  base. 

Tall  steel  cylinders  filled  with  concrete  and  well  braced  between  make  an 
economical  substructure  for  light  highway  bridges;  and  this  type  of  con- 
struction is  proper,  provided  that  the  cylinders  be  carried  far  enough  down 
into  fairly-hard  material  to  hold  firmly  the  lower  ends,  so  as  to  enable  the 
cylinders  to  act  as  beams  with  fixed  ends  for  resisting  the  bending  effects 
of  wind  loads  and  traction  loads.  Generally  in  such  cases  it  will  be  foimd 
necessary  to  build  a  substantial  mattress  around  each  pier,  so  as  to  prevent 
the  scouring  out  of  the  material  upon  which  reliance  is  being  placed  for 
fixing  the  ends. 

Temporary  piers  of  timber,  such  as  those  built  by  the  author  in  the 
middle  nineties  for  the  Missouri  Iliver  bridge  between  Council  Bluff's, 
Iowa,  and  l^^ast  Omaha,  Nel^raska,  are  a  k^gitimate  economic  expedient,, 
provided  that  (hw.  arrangement  be  made  for  replacing  them  later  l)y  ])er- 
manent  piers  without  involving  any  unnecessary  expense  or  inteiiupting 


ECONOMICS   OF   SUBSTRUCTURES  169 

traffic.  In  building  a  new  railroad  through  timber  country  it  is  in  the  line 
of  true  economy  to  put  steel  spans  temporarily  on  pile  piers  in  order  to 
avoid  the  excessive  cost  of  hauling  in  substructure  materials  before  the 
track  reaches  the  site.  In  such  cases  the  temporary  piers  should  be  located 
far  enough  from  the  positions  of  the  permanent  piers  to  allow  the  latter 
to  be  constructed  without  interfering  with  traffic. 

The  employment  of  the  cocked  hat  in  pier  shafts  is  generally  an  archi- 
tectural extravagance  that  should  be  avoided  whenever  its  use  is  not 
demanded  by  the  necessity  for  spreading  the  base  over  a  wide  pile  founda- 
tion. It  certainly  relieves  the  monotony  of  appearance  in  a  tall  shaft, 
but  the  principles  of  economy  generally  bar  it  out.  Only  once  in  the 
author's  career  has  he  ever  been  guilty  of  adopting  the  cocked  hat,  viz.,  in 
the  late  eighties  when  he  made  the  design  for  what  was  then  termed  the 
Winner  Bridge  over  the  Missouri  River  at  Kansas  City,  the  spans  of  which 
were  proportioned  to  carry  between  the  trusses  a  single-track  railway  with 
a  narrow  foot-walk  on  each  side  and  a  single-track  roadway  outside  of  each 
truss,  thus  making  the  perpendicular  distance  between  central  planes  of 
trusses  twenty-five  (25)  feet.  It  proved  to  be  a  fortunate  thing  that  the 
cocked  hat  was  employed,  for  the  superstructure  of  the  Winner  Bridge  was 
never  erected,  because  of  lack  of  funds ;  and  when  the  double-deck,  double- 
track,  Fratt  Bridge  was  built  on  the  old  piers,  after  cutting  down  the 
shafts  to  an  elevation  of  ten  feet  above  high-water  mark,  the  extra  length  of 
pier  afforded  by  the  said  cocked  hat  provided  just  the  necessary  extra  size 
for  permitting  the  superstructure  to  be  widened  sufficiently  to  carry  the 
double  track. 

Ice  breakers  are  sometimes  used  where  there  is  no  real  need  for  them, 
because  it  takes  an  enormous  amount  of  thick  ice  to  damage  any  well- 
founded  pier  having  a  shaft  with  rounded  ends;  nor,  as  a  rule,  does  a  con- 
crete pier  require  special  protection  against  the  grinding  of  ice.  If  real 
granitoid  of  one-two-three  composition  with  ten  per  cent  of  hydrated  lime 
added  to  the  cement  were  substituted  for  the  ordinary  concrete  between 
high-water  and  low-water  marks  and  extending  into  the  mass  about 
twelve  inches,  the  protection  thus  afforded  would  almost  always  be  ample 
and  would  involve  very  little  additional  expense.  Moreover,  the  repairing 
of  an  abraded  pier-surface  by  means  of  granitoid  is  not  a  difficult  matter. 
Unless  a  pier  rest  on  bed  rock,  the  placing  of  an  unbalanced  ice-break  upon 
it  is  going  to  upset  the  equality  of  load  distribution  over  the  foundations 
and  thus,  possibly,  cause  trouble.  In  case  of  a  pier  on  piles,  it  would  be 
better  to  put  another  ice-break  on  the  down-stream  end  of  the  pier  for  the 
sake  of  symmetry,  although  it  would  serve  no  useful  purpose  as  an  ice- 
break  per  se.  All  violations  of  the  precept  of  symmetry  are  to  be  avoided 
whenever  this  is  practicable;  for,  by  so  doing,  trouble  also  is  often  avoided. 

The  economic  question  of  reinforced-concrete  versus  timber  for  cribs  and 
caissons  is  beginning  to  loom  up.  At  the  same  total  first  cost,  timber  is 
preferable,  owing  to  the  ease  and  rapidity  with  which  it  may  be  put  in  place; 


170  ECONOMICS   OF   BRIDGEWORK  Chapter  XIX 

but  its  growing  scarcity  will  certainly  make  the  reinforced-concrete  shells 
of  such  constructions  more  and  more  popular  among  bridge  builders  as 
the  years  go  by.  In  using  it,  the  time  required  to  let  the  concrete  set  and 
harden  is  Hable  to  cause  delay  in  the  sinking;  and  the  removal  of  the  forms 
is  often  troublesome. 

This  last  statement  leads  to  the  thought  that  there  is  coming  up  soon 
the  economic  question  of  steel  versus  timber  for  concrete  forms.  At  present 
the  former  material  is  not  much  employed  for  this  purpose,  but  its  adoption 
therefor  is  on  the  increase,  especially  when  the  forms  have  to  be  used  a 
number  of  times.  After  timber  has  been  utilized  for  this  purpose  three  or 
four  times  it  becomes  badly  broken  up  and  unfit  for  further  service,  while 
the  steel  forms  with  care  can  be  used  an  indefinitely  great  number  of  times. 
A  combination  of  the  two  materials  might  be  employed  to  advantage,  the 
steel  being  interposed  between  the  concrete  and  the  timber  girders,  thus 
avoiding  injury  to  the  latter  and  permitting  them  to  be  used  over  and  over 
again. 

In  respect  to  the  depth  below  extreme  low  water  to  which  it  is  economic 
to  carry  the  shaft  of  a  pier,  there  is  great  difference  of  opinion  amongst 
engineers.  The  author  generally  locates  the  plane  of  division  between 
shaft  and  base  at  an  elevation  of  two  feet  below  the  lowest-recorded  water- 
level,  thus  providing  against  exposure  to  the  air  of  water-soaked  timber, 
even  in  seasons  of  abnormal  drought.  Such  treatment  for  a  short  time 
would  probably  do  no  harm,  but  the  exposure  of  the  crib  to  vision  is  not 
pleasing.  Those  who  claim  economy  for  locating  this  division  plane  far 
below  the  water's  surface  do  so  on  the  plea  that  it  requires  less  material. 
This  is  true  enough,  but  the  unit  price  of  the  portion  of  the  shaft  below  low- 
water  is  far  higher  than  that  above  the  same,  and  generally  somewhat 
greater  than  that  of  the  top  of  the  crib  itself.  For  tliis  there  are  several 
reasons,  viz.: 

First.  In  order  to  build  it,  a  fairly-water-tight,  removable  cofferdam 
has  to  be  constructed,  which  is  certainly  more  expensive  than  the  simple 
crib-top. 

Second.  This  cofferdam  has  to  be  kept  pumped  clear  of  water  until 
after  the  shaft  is  built. 

Third.  The  form-work  below  low-water  is  expensive  and  adds  mate- 
rially to  the  unit  cost  of  the  shaft-concrete. 

Fourth.  Where  the  shafts  are  carried  down  deep,  more  allowance  has 
to  be  made  for  possible  error  of  position;  and  to  do  this  would  involve  the 
enlarging  of  the  area  of  the  base,  thus  increasing  the  total  cost. 

The  (condition  sometimes  exists  which  calls  for  the  least  possible 
obstruction  of  the  waterway,  and  then  it  often  becomes  neccssarj^  to 
carry  the  shaft  down  to  the  bottom  of  the  channel,  irrespective  of  the 
extra  cost  of  the  piers.  In  such  cases  it  will  be  found  that  the  unit  value 
of  the  shaft-concrete  will  be  high,  and  that,  as  far  as  mere  cost  is  conccirned, 
it  would  have  been  better  to  carry  the  cribs  up  to  near  low-water  mark. 


ECONOMICS  OF  SUBSTRUCTURES  171 

The  determination  of  the  proper  clearance  to  allow  between  the  bottom 
of  the  shaft  and  the  inside  of  the  timber  or  reinforced-concrete  shell  is  an 
economic  problem  of  importance.  If  it  be  made  unnecessarily  large,  the 
volume  of  the  base  will  be  too  great  and  the  construction  too  costly.  On 
the  other  hand,  if  it  be  made  too  small  and  an  error  in  location  should 
occur  because  of  unanticipated  trouble  in  sinking,  it  would  be  difficult  to 
shift  the  shaft  the  right  amount  on  top  of  the  crib  in  order  to  get  it  into 
correct  position;  and  this  would  involve  delay,  than  which  there  is  nothing 
more  expensive  in  substructure  construction.  It  is  evident  that  one  must 
endeavor  to  strike  a  happy  mean  in  designing  his  cribs  and  caissons — but 
what  is  that  mean?  The  author's  practice  is  to  allow  as  a  minimum  a  foot 
clear  all  around  the  base  of  the  shaft  for  easy  conditions  of  sinking,  and  to 
increase  this  gradually  as  the  said  conditions  become  more  and  more 
unfavorable,  up  to  a  hmit  of  about  twice  that  amount.  It  would  certainly 
be  a  case  of  either  gross  carelessness  or  extremely  hard  luck  which  would 
prevent  the  correct  location  of  a  pier-shaft  when  the  larger  allowance-limit 
for  shifting  was  provided.  With  due  care  in  sinking,  the  error  of  position 
of  a  crib-top  should  seldom  exceed  a  few  inches;  consequently,  when  a 
bridge  engineer,  in  order  to  be  surely  on  the  safe  side,  makes  an  abnormally- 
great  allowance  for  error  of  crib  position,  he  does  so  at  the  expense  of  the 
work,  and  therefore  imperils  his  reputation  as  a  true  economist. 

Whether  to  use  the  pneumatic  process  instead  of  either  open-dredging 
or  cofferdam  excavation  is  fundamentally  an  economic  problem  based 
upon  the  theory  of  probabilities.  Comparing  the  open-dredging  and  the 
pneumatic  methods  of  sinking,  while  the  former  generally  figures  out  to  be 
the  cheaper,  its  cost  is  rather  uncertain,  because  of  the  possibility  of  encoun- 
tering large  logs  or  boulders;  and,  while  the  cost  of  installation  of  a  pneu- 
matic plant  adds  some  two  or  three  dollars  to  the  cost  per  cubic  yard  of  the 
bases,  one  can  count  almost  with  certainty  upon  the  total  expense  involved 
in  the  sinking.  If  bed  rock  be  within  reach  by  the  pneumatic  process,  that 
method  of  sinking  should  always  be  adopted,  unless  it  be  decided  not  to  go 
that  far  down  for  a  foundation,  in  which  case  the  open-dredging  process  is 
likely  to  be  the  more  economic.  One  should  never  sink  a  caisson  to  bed 
rock  by  open-dredging  for  fear  that  it  will  rest  on  one  edge  or  one  corner 
only  and  thus  provide  an  unequal  bearing.  It  would  be  far  better  to  stop 
short  of  it  a  small  distance  and  rest  on  sand,  gravel,  or  boulders  overlying 
the  rock. 

Comparing  the  cofferdam  method  with  that  of  open-dredging  into  a 
clay  or  other  fairly-hard  foundation-material,  unless  the  depth  below  the 
working  stage  of  water  be  less  than  eighteen  (18)  or  twenty  (20)  feet,  the 
latter  usually  is  preferable,  because  the  former  is  likely  to  give  trouble  and 
nearly  always  involves  a  greater  expenditure  of  money  than  that  allowed  in 
the  preliminary  estimate. 

The  economics  of  steel  sheet  piling  for  cofferdams  is  still  an  unsettled 
question  among  bridge  engineers.     Some  of  the  old-time  substructure  con- 


172  ECONOMICS   OF  BRIDGEWORK  Chapter  XIX 

tractors  contend  that  cofferdam  piers  sunk  by  their  use  are  more  expensive 
than  those  placed  by  the  pneumatic  process;  whilst  other  contractors, 
equally  experienced,  declare  the  contrary,  all  however  agreeing  that  the 
difference  in  cost  by  the  two  methods  is  small.  The  author  is  inclined  to 
believe  that,  if  a  thorough  set  of  borings  has  failed  to  indicate  any  sunken 
logs,  beds  of  large  boulders,  quicksand,  or  other  serious  impediment  to 
driving  or  excavating,  the  steel  sheet-piling  will  involve  a  moderate  saving 
in  first  cost  for  depths  of  foundation  below  ordinary  low  water  as  great  as 
forty  feet.  To  effect  such  a  saving,  however,  requires  an  experienced  and 
energetic  contractor  or  superintendent;  piling  of  ample  size,  thickness,  and 
length;  sufficient  of  it  for  three,  four,  or  even  five  piers  (according  to  the 
size  of  the  job),  with  extra  pieces  to  provide  for  damage  in  driving;  heavy 
pile-driving  hammers;  ample  pumping  capacity;  and  a  full  supply  of 
derricks,  engines,  and  other  outfit.  Generally,  it  is  the  small-fry  contractor 
who  prefers  the  cofferdam  method  to  the  pneumatic ;  and  he  is  tha  one  who 
is  most  likely  to  get  into  trouble  from  failure  to  anticipate  and  provide 
against  difficulties  in  driving  and  excavating.  His  pseudo-economic  dis- 
position leads  hi  n  into  purchasing  small,  thin,  and  short  piles;  for  he  does 
not  recognize  that  large  ones  will  withstand  battering  at  both  top  and  bot- 
tom much  better  than  small  ones,  that  thin  webs  are  liable  to  be  split  and 
bent  by  striking  large,  hard  boulders,  and  that  short  lengths  are  almost 
sure  to  involve  not  only  flooding  the  dams  but  also  filling  them  with  sand 
or  silt— possibly  several  times  during  the  progress  of  the  work. 

Steel-pile  cofferdams  have  been  successfully  used  for  depths  as  great  as 
fifty  feet  below  ordinary-low-water  elevation;  but  the  conditions  were  unu- 
sually favorable,  the  material  penetrated  being  mostly  soft  clay  that  shut 
out  the  water  almost  completely,  thus  enabling  bed  rock  to  be  reached  at 
moderate  expense. 

Large,  strong  sheet-piles,  in  addition  to  the  security  against  injury  in 
driving  which  they  provide,  effect  an  economy  by  permitting  the  waling 
frames  to  be  placed  farther  apart,  thus  lessening  the  amount  of  timber 
to  be  bought  and  the  expense  of  both  its  placement  and  its  removal ;  besides 
the  metal  often,  has  more  than  merely  scrap  value  at  the  end  of  the  job, 
which  is  seldom  the  case  when  small,  light  sections  are  employed. 

Sunken  logs  or  wrecks  give  endless  trouble  when  encountered  in  coffer- 
darn  work,  as  usually  they  have  to  be  shattered  to  splinters  by  dynamite 
before  the  piling  can  penetrate  them;  and  under  such  conditions  the  steel 
sh{;ct-piling  is  decidedly  superior  to  the  wooden  Wakefield-piling.  The 
lattei-  is  advantageous  for  shallow  excavations  and  for  cases  where  the  bed 
roclc  is  too  hard  to  penetrate;  because  the  ends  of  the  piles  broom,  and  the 
l)att(!re(l  wood,  by  absorbing  water,  expands  and  seals  the  bottom  of 
the  pit. 

T'lu!  cofferdam  method  is  spocinlly  applicable  where  clay  overlies  the 
IxmI  rof'k;  for  it  will  seal  the  bottom  of  the  l)ox.  Where  there  is  no  such 
scaling  lay(!r,  it  is  oft(;n  necessary  to  place  clay,  manure,  or  some  other 


ECONOMICS   OF   SUBSTRUCTURES  173 

material  on  the  outside,  or  else  to  employ  a  double-wall  cofferdam  filled  with 
clay. 

In  relation  to  the  comparative  economics  of  a  caisson,  put  down  by 
open-dredging  to  a  depth  that  is  absolutely  great  enough  to  insure  against 
disaster  from  scour,  and  a  crib  sunk  to  a  reasonable  depth  and  filled  with 
long  piles,  the  latter  generally  will  be  found  to  be  much  less  expensive;  but 
cases  will  occasionally  occur  when  the  reverse  is  true,  hence  it  is  well  always 
to  make  complete  comparative  estimates  of  cost.  These  require  only  a 
few  minutes'  work  for  an  experienced  bridge  computer. 

Once  in  a  while  it  occurs  that  the  pneumatic  process  has  to  be  employed 
for  one  or  more  piers  of  a  long  bridge,  the  others  being  sunk  by  open- 
dredging.  The  question  then  arises  as  to  how  many  to  put  down  by  the 
more  expensive  process ;  and  it  should  be  solved  more  with  reference  to  the 
expediting  of  the  construction  than  to  using  pneumatics  only  where  actu- 
ally required.  For  instance,  if  all  the  piers  but  one  could  be  handled  by 
open-dredging,  it  would  be  found  that  the  unit  price  for  the  base  of  that  one 
would  run  extravagantly  high,  because  it  would  have  to  take  care  of  a 
large  overhead  charge  for  use  and  transportation  both  to  and  fro  of  the 
pneumatic  machinery  and  other  outfit.  In  that  case  one  should  figure  how 
much  it  would  actually  cost  to  put  down  another  pier  by  pneumatics 
when  everything  necessary  is  on  the  ground  and  ready  to  move  over  to 
the  site  of  the  next  pier,  then  compare  the  result  with  the  cost  of  that  pier 
sunk  by  open-dredging.  Generally  but  httle  difference  will  be  found, 
and,  therefore,  it  might  prove  truly  economic  to  keep  both  outfits  occupied. 

The  sooner  any  piece  of  bridge  construction  is  finished,  the  sooner  will 
the  erection  contractor  be  ready  to  undertake  another  contract — besides 
it  is  often  the  case  that  an  expeditious  handhng  of  the  work  will  avoid  a 
rise  of  river  or  the  advent  of  other  unfavorable  working  conditions.  It  is, 
therefore,  logical  to  conclude  as  a  general  proposition  that  the  harder  a 
contractor  drives  his  work  the  more  money  will  he  net  from  his  operations, 
even  if  it  appear  to  the  casual  observer  that  he  is  spending  cash  rather 
recklessly  for  the  purpose  of  finishing  the  work  quickly.  Of  course,  if  the 
contractor  is  absolutely  sure  that  he  will  have  no  work  at  all  to  keep  his 
force  occupied  after  a  certain  job  that  he  is  on  is  completed,  it  will  not  pay 
him  to  spend  any  extra  money  to  rush  it;  but,  on  the  other  hand,  there  is 
nothing  to  be  gained  by  dragging  it  out  unnecessarily.  It  would  be  better 
to  finish  it  and  trust  to  luck  about  getting  another  contract. 

In  foundations  for  trestles  there  sometimes  arises  the  economic  question 
whether,  in  order  to  obtain  the  requisite  bearing  area,  it  would  be  better 
to  use  plain  concrete  and  go  rather  deep  by  stepping  off  the  base  in  the  old- 
fashioned  way,  or  to  spread  out  quickly  by  adopting  reinforcem.ent.  The 
surest  way  to  settle  the  question  is  to  proportion  a  pedestal  or  two  by  each 
method  and  compare  results.  If  for  any  reason  the  cost  of  the  excavation 
should  run  high,  the  reinforcement  method  will  have  a  decided  advantage. 
Again,  as  the  volume  of  the  concrete  is  much  smaller  for  that  type  of  base 


174  ECONOMICS  OF  BRIDGEWORK  Chapter  XIX 

than  for  the  other,  the  total  load  on  the  foundation  is  less,  and,  conse- 
quently, the  area  of  base  required  is  smaller.  Whether  the  excavation  is 
wet  or  dry  will  make  considerable  difference,  the  former  condition  favoring 
reinforcing  and  the  latter  militating  for  plain  concrete.  Where  the  footing 
cannot  be  pumped  out,  it  is  rarely  permissible  to  use  reinforcement. 

Sometimes  in  a  long  trestle  it  is  doubtful  whether  to  adopt  reinforced- 
concrete  piles  with  quite-shallow  bases  for  the  pedestals  or  to  employ  the 
cheaper  wooden  piles  and  sink  the  said  bases  to  extreme-low-water  eleva- 
tion, in  order  to  ensure  that  the  wood  shall  always  be  saturated  and  never 
exposed  to  the  air.  In  such  a  case,  one  or  two  pedestals  should  be  designed 
by  each  method  and  their  costs  determined  for  comparison. 


CHAPTER  XX 

ECONOMICS    OF   TRUSSES   AND    GIRDERS 

During  the  last  half  century  several  treatises  have  been  written  upon 
the  subject  of  economy  in  superstructure  design,  but  unfortunately  the 
result  is  simply  a  waste  of  good  mental  energy;  for  the  writers  tiiereof 
invariably  attack  the  problem  by  means  of  complicated  mathematical 
investigations,  not  recognizing  the  fact  that  the  questions  they  endeavor  to 
solve  are  altogether  too  intricate  to  be  undertaken  by  mathematics.  The 
object  of  each  investigation  appears  to  have  been  to  establish  an  equation 
for  the  economic  depth  of  truss,  or  that  depth  which  corresponds  to  the 
minimum  amount  of  metal  required  for  the  said  truss;  and,  to  start  the 
investigation,  it  seems  to  have  been  customary  to  make  certain  assumptions 
which  are  not  even  approximately  correct.  For  instance,  the  principal 
assumption  of  several  treatises  in  French  and  English  is  that  the  sectional 
area  and  the  weight  of  each  member  of  a  truss  are  directly  proportional  to 
its  greatest  stress;  or,  in  other  words,  that  in  proportioning  all  members  of 
trusses  a  constant  intensity  of  working  stress  is  to  be  used,  while  in  reality 
for  modern  steel  bridges  the  intensities  often  vary  considerably  in  the  same 
specifications.  Again,  no  distinction  is  made  between  tension  and  com- 
pression members,  and  no  account  is  taken  of  the  greatly  varying  amounts 
of  their  percentages  of  weights  of  details. 

There  is,  however,  one  mathematical  investigation  concerning  economic 
truss  depths  which  is  approximately  correct,  and  which  is  based  on  assump- 
tions that  are  very  nearly  true ;  but  it  holds  good  only  for  trusses  with  par- 
allel chords.     It  is  this: 

Let  A  =  weight  of  the  chords, 
5  =  weight  of  the  web, 
C  =  weight  of  the  truss, 
and       D  =  depth  of  the  truss. 

Then 

C  =  A-\-B.  [Eq.  1] 

But  the  weight  of  the  chords  varies  inversely  as  the  depth,  or  A=j:, 
and  the  weight  of  the  web  varies  directly  as  the  depth,  or  B  =  bD,  where  a 
and  h  are  constants;  and,  therefore,  C  =  j:-\-bD. 

175 


176  ECONOMICS   OF   BRIDGEWORK  Chapter  XX 

If  C  is  to  be  made  a  mimmum,  we  shall  have,  by  dLfferentiation, 

^■=-^  +  "  =  0.  [Eq.2] 

or 

-^+^-=0,  or  A=B.  [Eq.3] 

As  the  second  differential  coefficient,  after  substitution  according  to  the 
usual  method  of  maxima  and  minima,  comes  out  positive,  the  result 
obtained  corresponds  to  a  minimum.  From  this  it  is  evident  that,  for 
trusses  with  parallel  chords,  the  greatest  economy  of  material  wiU  prevail 
when  the  weight  of  the  chords  is  equal  to  the  weight  of  the  web.  The 
author  has  verified  this  conclusion  by  checking  the  weights  of  chords  and 
webs  in  a  number  of  finished  designs,  finding  it  to  be  absolutely  reliable. 
However,  it  is  not  of  much  practical  value,  because  the  economic  depths  of 
trusses  with  parallel  chords  are  pretty  well  known;  and,  again,  when  spans 
are  in  excess  of  175  or  200  feet,  the  chords  of  through-bridges  are  seldom 
made  parallel.  Moreover,  the  best  depth  to  use  is  not  often  the  one  which 
gives  the  least  weight  of  metal  in  the  trusses. 

It  has  been  found  by  experience  that,  for  trusses  with  polygonal  top 
chords,  the  economic  depths,  as  far  as  weight  of  metal  is  concerned,  are 
generally  much  greater  than  certain  important  conditions  wiU  permit  to 
be  used.  For  instance,  especially  in  single-track,  pin-connected  bridges, 
after  a  certain  truss  depth  is  exceeded,  the  overturning  effect  of  the  wind- 
pressure  is  so  great  as  to  reduce  the  dead-load  tension  on  the  windward 
bottom  chord  to  such  an  extent  that  the  compression  from  the  wind  load 
carried  by  the  lower  lateral  system  causes  reversion  of  stress,  and  such 
reversion  eye-bars  are  not  adapted  to  withstand.  A  very  deep  truss 
reciuires  an  expensive  traveler,  and  decreasing  the  theoretically  economic 
depth  increases  the  weight  but  sHghtly;  hence  it  is  really  economical  to 
reduce  the  depth  of  both  truss  and  traveler.  Again,  the  total  cost  of  a 
structure  does  not  vary  directly  as  the  total  weight  of  metal,  for  the  reason 
that  an  increase  in  the  sectional  area  of  a  piece  adds  nothing  to  the  cost  of 
its  manufacture,  and  but  little  to  the  cost  of  erection;  consequently  it  is 
only  for  raw  material  and  freight  that  the  expense  is  reaUy  augmented. 
Hence  it  is  generally  best  to  use  truss  depths  considerably  less  than  those 
which  would  require  the  minimum  amount  of  metal.  For  parallel  chords, 
the  theoretically  economic  truss-depths  vary  from  one-fifth  of  the  span  for 
spans  of  100  feet  to  about  one-sixth  of  the  sjxxn  for  spans  of  200  feet;  but 
for  modern  single-track-railway  through-bridges  the  least  allowable  truss- 
depth  is  about  30  feet,  unless  suspended  floor-lieams  be  used,  a  detail  which 
very  properly  has  gone  out  of  fashion. 

In  two  fivc-hund red-foot  spans  of  a  combined  railway  and  highway 
l)ri(lg(!  the  author  employed  a  truss  depth  of  seventy-two  feet;  Imt  this  was 
determined  by  the  reversal  of  stress  in  bottom  chords    through  wind- 


ECONOMICS    OF   TRUSSES   AND   GIRDERS  177 

pressure.  A  greater  depth,  if  permissible,  would  have  caused  a  saving  in 
total  weight  of  metal.  In  another  of  his  designs  for  a  five-hundred-and 
sixty-foot  span  a  truss  depth  of  ninety  feet  was  adopted,  but  in  this  case  the 
live  load  was  very  great,  varying  fi'om  ten  thousand  pounds  per  lineal  foot 
for  short  spans  to  eight  thousand  pounds  per  lineal  foot  for  long  ones; 
and  the  bridge  is  twenty  per  cent  wider  than  in  the  case  of  the  two  five- 
hundred-foot  spans  just  mentioned.  The  greater  the  live  load  and  the 
wider  the  bridge,  the  greater  generally  can  the  truss  depth  be  made  advan- 
tageously. 

The  little  mathematical  investigation  given  in  this  chapter  can  be 
applied  with  fair  accuracy  to  plate-girder  bridges  and  to  the  floor  systems  of 
truss-bridges.  If,  for  ordinary  cases,  in  designing  plate  girders,  one  will 
adopt  such  a  depth  as  will  make  the  total  weight  of  the  web  with  its  splice- 
plates  and  stiffening  angles  about  equal  to  the  weight  of  the  flanges,  he  will 
obtain  an  economically  designed  girder,  and  a  deep  and  stiff  one.  For 
long  spans,  however,  this  arrangement  would  make  the  girders  so  deep  as 
to  become  clumsy  and  expensive  to  handle;  consequently,  when  a  span 
exceeds  about  forty  feet,  the  amount  of  metal  in  the  flanges  should  be  a 
little  greater  than  that  in  the  web ;  and  the  more  the  span  exceeds  forty  feet 
the  greater  should  be  the  relative  amount  of  metal  in  the  flanges. 

The  true  economic  investigation  for  plate-girders  is  as  follows,  when  the 
web  is  assumed  to  resist  its  share  of  the  bending  moment : 

Let  M  =  bending  moment  at  mid-span, 
h   =  depth  of  web, 
t    =  thickness  of  web, 

S  =  intensity  of  working  stress  for  tension, 
I    =  length  of  span, 
and        c   =  ratio  of  weight  of  details  of  web  (i.e.,  end  stiff eners,  inter- 
mediate stiffeners,  splice  plates,  and  fillers)  to  weight  of  the  web  plate  itself. 

The  sum  of  the  two  flange  areas  at  mid-span,  including  an  allowance  of 
fifteen  per  cent  for  rivet  holes,  will  be  given  by  the  equation, 

F=1.15(^^-lhty,  [Eq.4] 

and  the  total  weight  of  metal  in  the  flanges,  taking  into  account  the  fact 
that  the  cover  plates  do  not  run  the  full  length  of  the  girder,  will  be  given 
approximately  by  the  equation. 


/2Af     1      \ 
Wf=3AXl.l5ij^-^ht]  X0.8  l. 


1  84  M 
=  3.4  Z  ( -^^ 0.23  ht ) .  [Eq.  5] 


hS 
The  weight  of  the  web  and  its  details  will  be 

W^  =  3.4:l(ht-\-cht).  [Eq.  6] 


178  ECONOMICS   OF  BRIDGEWORK  Chapter  XX 

Therefore  the  total  weight  of  girder  will  be 

=  3.4  //^-^^^+0.77  U+cht\.  [Eq.  7] 

Differeritiating  with  respect  to  h  and  placing  the  differential  coefficient 
equal  to  zero  gives 

/     1  84  M  \ 

=  3.4  ?(  -^^^p+0.77  t+ct\  -0.  [Eq.  8] 

=  0.77  ht-{-cht;  [Eq.  9] 


dWo    .  _/     1.84  M 
dh 
Hence 

1.84  U 

hS 


from  which  we  find 

1  84  M 
Vl     -0.23  ht^OM  ht^cht,  [Eq.  10] 

and 

3.4  l0^^^-0.23  hi)  =3.4  Z(0.54  ht-\-cht).  [Eq.  11] 

But  the  value  of  c  is  generally  about  0.3.     Substituting  this  gives 

3.4  ^("-^^-0.23 /iA  =3.4  Z(0.84/i0.  [Eq.  12] 

But  the  first  member  of  this  equation  represents  the  weight  of  the  flanges 
for  the  most  economic  condition,  and  the  second  member  is  eighty-four 
per  cent  of  the  total  weight  of  the  web  plate  without  its  details. 

Dividing  both  sides  of  the  last  equation  by  0.8  and  canceling  the  3.4  I 
gives 

/O  Q   /If  \ 

(^1^-0.29  ht)  =  1.05  ht,  [Eq.  13] 

or 

1.15(^^-0.25  ht\  =  1.05  ht.  [Eq.  14] 

Evidently  the  first  member  of  this  equation  represents  the  gross  area  of  the 
flanges  and  the  second  member  differs  only  a  little  from  the  gross  area  of 
the  w(^b  and  may  without  any  great  error  be  called  such.  Hence  it  may  be 
stated  that  the  theoretical  maximum  of  economy  exists  when  the  gross 
areas  of  flanges  and  of  web  at  mid-span  are  equal — a  condition  readily 
remembered.  If  the  depth  of  web  be  selected  on  this  basis,  rather  than  by 
the  old  criterion  which  makes  the  total  weight  of  flanges  equal  to  the  total 
weight  of  web  with  all  its  details,  it  will  be  found  to  give  a  greater  web 
depth.  This  increased  depth  is  likely  to  augment  the  cost  from  one  or  more 
of  the  following  practical  considerations  which  the  formula  cannot  take 
into  account: 


ECONOMICS    OF   TRUSSES   AND    GIRDERS  179 

A.  An  additional  splice  or  two  in  the  web,  or  else  a  slightly  increased 
pound  price  for  the  large  plates. 

B.  Larger  outstanding  legs  for  all  stiffening  angles. 

C.  Reduction  in  the  number  of  cover  plates. 

D.  Narrowing  of  flange  angles  and  necessitating  thereby  either  an 
additional  bracing  frame  or  an  increase  in  sectional  area  of  the  compression 
flange,  in  order  to  compensate  for  the  greater  ratio  of  unsupported  length  to 
width. 

E.  Possible  thickening  of  web  because  of  its  greater  depth. 

F.  Possible  encroachment  on  under-clearance  in  deck  spans,  or  raising 
of  grade  to  avoid  the  same. 

G.  Possible  difficulty  in  fabrication  or  shipment  in  case  of  long  or 
heavy  girders  because  of  excessive  depth. 

Any  one  of  these  changes  would  be  likely  so  to  upset  the  economics  of 
the  case  as  to  cause  material  decrease  in  the  theoretical  depth  found  by  the 
preceding  investigation.  One  will  not  often  make  an  error  in  economy  by 
following  the  old  established  rule  in  "  De  Pontibus  "  to  the  effect  that  the 
best  practicable  arrangement  is  generally  to  make  the  weight  of  the  flanges 
equal  to  the  weight  of  the  web  and  its  details;  and  there  are  occasionally 
cases  where  a  saving  of  metal  can  be  effected  by  making  the  web  depth  even 
smaller  than  that  given  by  this  old  criterion,  when  by  so  doing  a  web  splice 
may  be  avoided  or  smaller  stiffening  angles  may  be  adopted.  It  should  be 
borne  in  mind  that  there  is  quite  a  range  in  web  depths  over  which  the 
theoretic  minimum  weight  is  about  constant,  unless  the  thickness  of  the 
shallower  web  must  be  increased  on  account  of  the  shear;  hence  one  may 
often  vary  the  dimensions  of  a  plate-girder  materially  without  affecting 
greatly  the  matter  of  economics.  In  Fig.  20a  is  given  a  diagram  of  eco- 
nomic depths  of  plate-girders  with  riveted  end  connections. 

Concerning  economic  panel  lengths  for  truss  bridges,  it  is  safe  to  make 
the  foflowing  statement:  Within  the  limit  set  by  good  judgment  and 
one's  inherent  sense  of  fitness,  the  longer  the  panel  the  greater  the  economy 
of  material  in  the  superstructure.  Of  course,  when  one  goes  to  such  an 
extent  as  to  use  a  thirty-foot  panel  in  an  ordinary  single-track-railway 
bridge  he  exceeds  the  limits  referred  to,  because  the  lateral  diagonals 
become  too  long,  and  their  inclination  to  the  chords  becomes  too  flat  for 
rigidity.  Again,  an  extremely  long  panel  might  sometimes  cause  the  truss 
diagonals  to  have  an  unsightly  appearance  on  account  of  their  small 
inclination  to  the  horizontal. 

In  plate-girder  structures  with  floor-system  of  cross-girders  and  string- 
ers, there  is  generally  no  economy  in  adopting  long  panels — in  fact  they  are 
certain  to  involve  an  increase  of  total  weight  of  metal;  but,  on  the  other 
hand,  the  cost  of  erection  is  probably  lessened  by  reducing  the  number  of 
field-driven  rivets. 

Warren  trusses  are  cheaper  than  Pratt  or  Petit  trusses  for  parallel  chords, 
but  not  for  those  with  a  polygonal  chord.     The  first-mentioned  type 


180 


ECONOMICS   OF   BRIDGEWORK 


Ch.^pter  XX 


changes  sectional  areas  of  chords  onlj^  one-half  as  often  as  do  the  others, 
which  feature  tends  to  save  metal  in  spUce  plates  and  expense  in  field 
riveting. 

The  length  of  span  at  which  it  pays  to  change  from  parallel  chords  to 
curved  or,  more  properlj'  speaking,  polygonal  chords,  will  vary  with  the 
class  of  bridge;  but  it  is  seldom  advisable  to  adopt  the  latter  for  spans 
under  two  hundred  feet.  The  greater  the  panel  length  the  greater  the 
Hmit  of  span  for  parallel  chords,  consequently  it  will  generally  be  found 
shorter  for  highway  bridges  than  for  railway  bridges.  This  curving  of  the 
tcp  chords  of  long  through-spans  has  sometimes  been  carried  to  such  excess 


/oooo 


/5G00 
J50 


Fig, 


O  5000  /OOOO  /SOOO 

Jb/a/l.  oej<^  /n  /^oancfs  perjL/nea/  /vofofG/rc^er 

20a.     Economic  Depths  of  Plate-Girders  witli  Kiveted  End-Connections. 


as  to  approach  very  closely  the  old  pai-abolic  trusses,  in  which  the  curve 
extends  from  end-pin  to  end-pin.  In  a  large  and  in'portant  bridge  over  the 
Mississippi  River  the  top  chords  of  the  main  spans,  which  exceed  five  hun- 
dred feet  in  lengtli,  are  so  curved  as  to  involve  the  use  of  a  very  shallow 
portal,  allowing  but  the  ordinary  clear  headway  beneath.  Such  excessive 
curvature  causes  the  top  chord  to  do  most  of  the  work  of  the  web  and  makes 
the  lattei-  too  light  and  vibratory.  It  also  necessitates  the  use  of  counters 
or  stiff  main  diagonals  almost  up  to  the  ends  of  the  span.  A  proper  curva- 
ture of  the  chords  is  not  only  economical  of  both  metal  and  money,  but  also 
is  iT'sthotic,  adding  greatly  to  the  appearance  of  most  bridges,  consequently 
this  featui-e  should  be  encouraged,  but  not,  of  course,  to  excess.  The  best 
curvature  of  chords  for  any  span  can  only  be  determined  by  experience, 


ECONOMICS   OF   TRUSSES   AND   GIRDERS  181 

the  controlling  factor  being  reversion  of  web  stresses.  In  general,  it  may  be 
said  that  the  greater  the  arching  the  more  artistic  the  effect.  For  highway 
bridges  it  can  be  made  greater  than  for  railway  bridges,  because  the  effect 
of  impact  is  less  in  the  former  than  in  the  latter;  nevertheless,  even  in  high- 
way bridges  the  curvature  must  not  be  carried  to  excess  on  account  of  the 
tendency  of  light  web  members  to  set  up  vibration  from  insignificant 
moving  loads. 


CHAPTER  XXI 

economics    of    decks    and    floor-systems 
Steam-Railway  Bridges 

Decks 

Railway-bridge  decks  may  be  of  timber  ties,  either  plain  or  treated, 
spaced  from  twelve  to  fifteen  inches  from  center  to  center,  with  either  two  or 
four  rows  of  wooden  guard-rails  bolted  thereto;  trough  floors  with  or 
without  ballast;  ballasted  road-bed  resting  on  a  solid  floor  of  treated 
planking,  steel  plate,  or  reinforced-concrete  slab;  or  rails  resting  directly 
on  the  steelwork. 

The  most  common  type,  and  the  cheapest,  as  far  as  fii'st  cost  is  con- 
cerned, is  the  open,  untreated-timber  deck;  but  it  maj^  be  more  expensive 
than  some  of  the  other  types  when  the  item  of  maintenance  is  considered. 
It  affords  easy  riding,  but  is  not  so  safe  against  derailment  or  burning. as 
decks  that  are  closed.  These  advantages  and  disadvantages,  however, 
cannot  be  evaluated  in  money.  Treated  ties,  of  .course,  cost  more  than  the 
plain  ones;  but  they  generally  last  so  much  longer  that  they  are  more 
economical  in  the  end.  They  can  be  of  a  cheaper  grade  of  tmiber  than 
the  untreated  ones,  but  this  saving  is  offset  by  the  necessity  for  using  tie 
plates  between  the  timber  and  the  rails.  Without  these  the  hfe  of  the  soft 
timber  would  be  very  short  under  heavy  traffic.  However,  first-class  con- 
struction calls  for  tie  plates  on  all  timber  ties. 

Trough  floors  with  ballast  and  ties  therein  are  uncommon.  This  was 
one  of  the  first  kinds  of  shallow  floor  to  be  built,  but  it  has  gone  out' of 
fashion.  There  was  one  tie  per  trough,  and  it  generally  rested  directly  on 
the  steel;  but  sometimes  a  few  inches  of  ballast  were  interposed.  This 
type  is  noisy  and  expensive,  and  the  replacement  of  ties  in  the  trough  is 
both  difficult  and  costly. 

Ballasted  decks  are  more  expensive  in  respect  to  first  cost  than  the  open 
ones,  especially  in  long-span  structures,  on  account  of  the  augmented  dead 
load.  They  provide  easier  riding;  and  for  short-span  bridges  on  first- 
class  lines  they  are  almost  exclusively  adopted  as  standard.  One  incidental 
advantage  that  they  possess  is  that  they  permit  the  use  of  skew  nbutments, 
which  are  not  compatible  with  the  open-timber  type  of  deck.  Again,  they 
are  more  conducive  to  maintenance  of  alignment;  and  they  protect  the 
steelwork  fairly  well  from  bi-ine  di-ippings. 

182 


ECONOMICS   OF   DECKS   AND    FLOOR-SYSTEMS  183 

The  cheapest  good  type  of  ballasted  floor  is  that  in  which  the  ballast 
rests  on  a  solid  base  of  creosoted  planks;  and  a  high  authority  on  railroad 
bridge  building  and  operation  claims  that,  considering  the  cost  of  mainte- 
nance, this  deck  is  cheaper  than  the  open-timber  one  for  spans  of  ordinary 
length.  It  would  be  very  uneconomical  to  omit  the  treatment  of  the 
timber;  because,  in  replacing  the  base,  it  is  necessary  to  remove  and  store 
the  ballast  and  later  to  put  it  back. 

Ballast  resting  directly  on  steel  plate  is  not  much  used,  although  it 
produces  a  shallow  deck,  which  is  sometimes  a  sine  qua  non.  It  is  expen- 
sive, and  the  steel  plate  is  hable  to  rust. 

Ballast  resting  on  a  reinforced-concrete  slab  represents  \he  highest 
grade  of  construction,  but  it  is  too  heavy  for  long  spans.  In  short  spans, 
weight  is  desirable  for  high  speed  so  as  to  check  vibration,  notwithstanding 
the  fact  that  the  cost  of  the  steelwork  is  increased  thereby.  It  is  the  best 
type  for  overhead  crossings  for  the  following  reasons — the  noise  is  reduced 
to  a  minimum,  it  can  be  built  waterproof  to  exclude  drippings,  the  depth 
can  be  made  comparatively  small,  and  the  maintenance  cost  is  the  least 
practicable.  This  style  of  deck  requires  a  specially-good  drainage  system; 
and,  if  the  steel  is  encased,  the  deck  must  be  waterproofed,  which  adds  to 
the  expense.  True  economy  calls  for  a  two-ply,  three-ply,  or  even  four- 
ply  membrane  of  cotton  drilling  or  burlap  covered  with  asphalt  of  the 
proper  consistency.  The  cotton  has  proved  to  be  more  durable  than 
the  burlap ;  and,  therefore,  it  is  the  more  economic.  It  is  advisable  for  the 
sake  of  durabihty  (and,  consequently,  for  that  of  economy)  to  cover  the 
waterproofing  with  either  protection-bricks  or  thin  concrete,  the  latter 
being  the  lighter  and  cheaper.  An  important  portion  of  the  work  is  the 
joint  of  the  flashing  with  the  web  of  the  girder.  This  requires  very  care- 
ful attention  in  both  design  and  construction,  if  leakage  is  to  be  prevented. 

Rails  laid  directly  on  the  steelwork  give  a  minimum  depth  for  the  floor, 
but  they  require  a  rather  expensive  floor-system;  and  there  being  no 
cushion  between  rails  and  steel  supports,  the  riding  is  not  easy  and  the  noise 
involved  is  excessive.  For  these  reasons  the  type  is  not  desirable ;  and  the 
only  excuse  for  using  it  is  a  compulsory  call  for  an  exceedingly  shallow  floor. 

Spans  without  Floor- Systems 

The  floor-system  proper  may  be  omitted  in  I-beam  spans,  most  deck 
plate-girder  spans,  those  half-through  plate-girder  spans  in  which  the 
wooden  ties  rest  on  either  the  bottom  flanges  of  the  main  girders  or  on  spe- 
cial shelf-angles,  and  short  deck  truss-spans  in  which  the  ties  are  sup- 
ported directly  by  the  top  chords.  This  omission  of  the  floor-system  is 
entirely  proper  from  the  points  of  view  of  both  economy  and  expediency, 
as  far  as  I-beam  and  deck  plate-girder  spans  are  concerned,  and  even  in  the 
case  of  deck  truss-spans  when  the  truss-spacing  is  not  too  wide.  Beyond 
the  limit  of  ten  feet  from  center  to  center  of  trusses  the  size  required  for  ties 


184  ECONOMICS    OF   BRIDGE  WORK  Chapter  XXI 

becomes  too  great  for  heavy  loadings.  It  is  true  that  this  hmit  is  some- 
times made  as  high  as  thirteen  feet;  but  then  the  ties  are  difficult  to  secure, 
and  the  maintenance  cost  thereof  is  large. 

Resting  ties  on  the  bottom  flanges  or  on  special  sheK-angles  in  half- 
through,  plate-girder  spans,  although  economic  in  first  cost,  is  not  good 
construction;  because  the  removal  and  replacement  of  the  said  ties  is 
abnormally  troublesome  and  expensive.  This  practice,  which  was  quite 
common  two  or  three  decades  ago,  is  pseudo-economical,  especially  in  view 
of  the  rapidly-augmenting  prices  of  timber.  Moreover,  this  detail  has  a 
tendency  to  distort  the  webs  of  the  girders;  and  the  depth  available  for 
cross-struts  is  small.  These  are  needed  for  a  proper  staying  of  the  top 
flanges  of  the  main  girders,  and  they  have  to  be  stiff  in  order  to  be  effective. 

Open  timber  decks  can  be  used  on  I-beam  spans,  on  deck,  plate-girder 
spans,  and  on  deck  truss-spans  without  floor-systems,  as  can  also  ballasted 
decks  supported  by  treated  timber  or  reinforced-concrete  slabs.  In  short 
I-beam  spans  the  beams  can  be  spaced  closely  and  a  thin  slab  can  be 
employed,  or  the  beams  can  be  embedded  in  the  slab,  or  there  can  be  used 
longitudinal,  reinforced-concrete  troughs  resting  on  the  bottom  flanges  of 
the  I-beams  with  the  latter  encased  in  concrete.  For  I-beam  spans  with 
either  timber  or  ballasted  deck,  it  is  cheapest  to  adopt  the  minimum  number 
of  beams  that  will  carry  the  load;  but  with  limited  headroom  it  will  be 
found  necessary  to  employ  shallow  beams  and  space  them  closely.  If 
it  be  desirable  for  the  sake  of  protection  to  encase  the  said  beams  in  con- 
crete, it  is  usually  most  economic  to  rest  the  slab  on  the  beams  and  encase 
them  separately;  but  for  very  thin  floors  it  is  cheapest  either  to  embed  the 
beams  in  the  solid  slab,  or  to  use  reinforced-concrete  troughs. 

Floor-Systems 

The  standard  floor-system  consists  of  two  stringers  per  track  riveted 
to  the  cross-girders,  with  the  latter  riveted  in  turn  to  the  trusses  or  main 
girders.  In  general,  this  construction  is  by  far  the  most  economic  type 
of  floor-system;  and  it  provides  substantial  floor-beams  at  panel  points 
to  serve  as  lateral  struts.  It  can  be  used  with  any  of  the  ordinary  types  of 
deck  previously  described.  Auxiliary  stringers,  often  termed  "jack- 
stringers,"  are  sometimes  added  so  as  to  take  care  of  derailed  trains. 
Four  carrying-stringers  per  track  are  occasionally  employed,  cither  because 
it  is  the  policy  of  the  road  to  do  so  or  in  order  to  permit  the  adoption  of  a 
shallow  floor,  especially  in  half-through,  plate-girder  spans.  It  is  more 
economic  to  adopt  four  lines  of  carrying-stringers  per  track  than  to  have 
only  two  of  them  and  two  lines  of  jack-stringers,  for  the  reason  that,  except 
in  the  case  of  derailment,  the  latter  are  idlers.  Four  carrying-stringers,  of 
course,  re(iuii'e  more  metal  than  do  two,  especially  with  long  paiK>ls;  but 
with  hallastcd  dc^cks  on  concrete  slabs  they  ])(Miuit  a  reduction  in  the  slab- 
tlii(;kn(\ss;  and  in  sjjans  of  considerable  length  I  he  reduction  in  dead  load 
involved  will  nearly  compensate  for  the  extra  stringer  metal. 


ECONOMICS    OF   DECKS   AND    FLOOR-SYSTEMS  185 

The  economic  panel  length  for  this  type  of  floor-system,  as  far  as  that 
floor-s,ystem  alone  is  concerned,  is  always  smaller  than  can  be  employed 
for  single-track  truss-bridges,  whether  through  or  deck,  as  can  be  seen  by 
referring  to  the  curves  on  pages  1224,  1229,  and  1233  of  "Bridge  Engineer- 
ing." This  is  also  true  for  double-track,  riveted-truss  biidges,  as  shown 
by  the  curves  on  page  1239  of  that  treatise,  although  there  is  no  great 
reduction  below  25  feet.  For  double-track,  pin-connected  bridges,  25 
feet  is  the  economic  length  (see  "  Bridge  Engineering,"  page  1244).  This 
is  due  to  the  extra  metal  required  for  the  cut-away  ends  of  the  floor-beams, 
making  pin-span  cross-girders  much  heavier  than  riveted-span  ones. 
Where  jack-stringers  or  four  lines  of  carrying-stringers  per  track  are 
employed,  the  economic  panel  lengths  would  be  still  shorter.  It  will  be 
found,  however,  that  variation  in  panel  length  will  not  affect  greatly  the 
total  weight  of  metal  in  span,  since  lengthening  the  panels  generally 
reduces  the  truss  weight.  For  long,  deep  trusses,  longer  panels  than 
usual  give  smaller  total  weights  of  truss  metal. 

In  respect  to  the  economic  depths  of  stringers  for  two  lines  per  track, 
they  vary  from  4  feet  for  20-foot  panels  to  5  feet  for  35-foot  panels  with 
light  live  loads,  and  from  5  feet  for  20-foot  panels  to  6  feet  for  35-foot 
panels  for  heavy  live  loads.  The  economic  depths  for  four  lines  of 
stringers  per  track  are  about  one  foot  less  than  the  preceding. 

The  economic  depths  for  floor-beams  vary  from  5  feet  to  6  feet,  accord- 
ing to  panel  length,  in  single-track  bridges  with  light  live  loads,  and  from 
6  feet  to,  7  feet  with  heavy  live  loads.  The  corresponding  figures  for 
double-track  bridges  are  respectively,  from  6  feet  to  8  feet,  and  from  8 
feet  to  10  feet. 

Under-clearance  requirements  often  call  for  shallower  floor-beams 
than  those  of  economic  depth,  especially  for  double-track  bridges.  Very 
shallow,  double-track,  railway-bridge  floor-beams  are  quite  expensive. 
Any  decrease  in  depth  of  floor-system  below  the  economic  one  will  increase 
the  cost  of  main  structure;  but  this  is  partially  ofi^set  by  the  slightly- 
reduced  lengths  of  approaches;  consequently,  when  comparing  the  costs 
of  floor-systems  of  different  depths,  this  fact  must  not  be  forgotten. 

Half-through,  plate-girder  spans  are  used  only  where  the  headroom  is 
Umited;  hence  the  floor-systems  for  these  structures  are  almost  always 
shallow  and  uneconomic  of  metal.  With  open-timber  decks,  four  lines  of 
carrying-stringers  per  track  are  employed  in  order  to  provide  a  shallow 
floor;  and  the  panels  can  be  short  and  of  economic  length.  Sohd  floors 
are  quite  common  with  through-plate-girder  construction.  The  trough 
floor-system  is  very  thin,  and  hence  is  appHcable  thereto;  but  it  is  expensive 
and  otherwise  objectionable,  as  hereinbefore  explained.  When  a  ballasted 
deck  on  creosoted  timber  is  adopted,  four  stringers  per  track  can  be  used, 
but  it  is  more  common  to  employ  closely-spaced,  transverse  rolled  I-beams, 
especially  when  the  headroom  beneath  is  small.  The  latter  construction 
is  also  usually  employed  with  a  ballasted  deck  carried  on  a  steel  plate. 


186  ECONOMICS   OF   BRIDGEWOKK  Ch.\pter  XXI 

Ballasted  decks  on  reinforced-concrete  slabs  are  much  used  for  half- 
through,  plate-girder  spans.  The  floor-system  can  be  of  the  usual  stringer- 
and-fioor-beam  type,  generally  with  four  lines  of  stringers  per  track, 
on  account  of  restricted  headroom;  or  the  slabs  can  rest  on  rather- 
closely-spaced,  transverse  beams.  With  the  latter  arrangement  it  is 
economic  of  metal  to  adopt  spacings  of  5  feet  or  more;  but,  on  account 
of  restricted  head  room,  it  is  frequently  necessary  to  space  much  more 
closely,  in  order  to  permit  the  use  of  shallower  beams.  If  the  available 
depth  is  very  small,  these  cross-beams  can  be  embedded  in  the  sohd 
slab;  or  reinforced-concrete  troughs  resting  on  the  bottom  flanges  of 
the  beams  can  be  employed,  the  tops  of  the  beams  being  encased  in 
concrete.  The  relative  economics  of  the  last  three  types  depend  on 
whether  the  steel  needs  to  be  encased  so  as  to  protect  it  from  locomotive 
blast  or  other  attack  from  below.  If  no  encasement  be  required,  the 
first  type  is  the  cheapest;  but  otherwise  there  is  not  much  difference  in 
the  costs  of  the  three.  As  before  mentioned,  in  all  cases  where  beams  are 
embedded  in  concrete,  the  top  surface  of  the  slab  must  be  water- 
proofed. 

Rails  resting  directly  on  the  steel  require  floor-systems  of  closely-spaced, 
transverse  beams — an  expensive  construction  and  not  good  in  case  of 
derailment. 

In  respect  to  encasement,  it  is  generally  economic  to  put  it  on  by 
cement-gun,  because  it  is  cheaper  than  the  poured  covering,  and  being 
thinner  it  saves  in  the  dead  load  to  be  carried  by  the  steelwork. 

For  double-track,  deck  truss-spans  it  is  most  economical  for  the  floor- 
system  to  space  the  trusses  20  feet  or  21  feet  centers,  and  to  use  two  lines 
of  stringers  about  7  feet  centers,  resting  the  ties  on  the  stringers  and  top 
chords.  Such  a  floor-system  weighs  but  little  more  than  that  for  a  single- 
track  through-bridge.  It  may  take  so  much  extra  metal  in  the  strength- 
ened chords  as  to  absorb  most  of  the  saving  from  the  omission  of  the  two 
lines  of  stringers,  but  the  floor  beams  are  much  lighter  than  those  ordi- 
narily required  for  double-track  bridges.  There  is  also  considerable 
economy  involved  in  the  lateral  system  and  vertical  sway  bracing.  In 
this  layout  of  floor-system  any  of  the  three  ordinary  types  of  deck  can 
be  utilized. 

In  general  it  may  be  stated  that  for  any  span-length  the  floor-system  of 
a  deck  span  will  be  cheaper  than  that  of  a  through  span. 

Stringers  are  usually  plate-girders,  except  for  through,  plate-girder 
spans;  and  in  these  rolled  I-beams  are  more  applicable.  Floor-beams 
are  nearly  always  plate-girders,  although  occasionally  in  narrow  structures 
it  may  pay  to  use  deep  rolled  I-beams.  Cross-beams  in  through,  plate- 
girder  spans  having  no  stringers  arc  nearly  always  rolled  I-bcams,  unless 
the  span  be  unusually  wide. 

In  making  economic  comparisons  between  plate-girder  and  rolled 
I-beam  constructions,  it  is  necessary  to  take  into  account  the  difference  in 


ECONOMICS   OF   DECKS   AND    FLOOR-SYSTEMS  187 

the  pound  prices  of  the  two  types,  the  said  difference  usually,  but  not 
always,  being  in  favor  of  the  latter. 

Electric  Railway  B^iiidges 

This  type  of  structure  is  found  on  interurban  roads  and  elevated 
railways.  The  economic  problems  of  the  deck  and  floor-system  are  sim- 
ilar to  those  in  steam-railway  structures,  except  that  the  construction  is 
much  lighter.  The  economic  lengths  are  somewhat  greater  because  the 
loads  are  smaller,  but  the  economic  principles  involved  are  identical. 

Highway  Bridges 
Decks 

For  highway  bridges  there  are  two  general  types  of  deck,  viz.,  timber 
and  concrete.  In  respect  to  first  cost  of  both  the  deck  itself  and  the 
material  required  to  support  its  weight,  the  timber  type  is  always  the 
cheaper,  the  saving  increasing  with  the  span  length.  In  times  past  the 
timber  deck  per  se  was  very  much  less  costly  than  the  concrete  deck,  but 
to-day  it  is  otherwise,  because  the  price  of  timber  has  risen  more  rapidly 
than  that  of  any  other  material  employed  in  bridge  construction.  Whether 
at  the  present  time  in  any  particular  case  timber  or  concrete  per  se  for  decks 
is  the  cheaper  will  depend  somewhat  upon  the  locahty  and  the  availability 
of  supply  for  the  various  materials.  The  solution  of  the  question  has  to 
be  determined  specially  for  each  case,  as  it  arises,  but  the  difference  in 
first  cost  for  the  two  types  will  seldom  be  found  great.  The  real  economic 
question  involved  is  one  of  comparative  weights  and  costs  of  the  materials 
required  to  carry  the  deck. 

When,  however,  maintenance  and  renewals  are  taken  into  considera- 
tion, the  concrete  deck  will  nearly  always  be  found  to  be  the  more  econom- 
ical for  short  spans  and  those  of  moderate  length.  There  is,  though,  one 
factor  of  vital  importance  that  cannot  well  be  considered  in  the  economic 
comparison,  viz.,  the  danger  from  fire.  This  is  so  important  as  to  rule  out 
the  use  of  timber  in  bridge  decks  for  aU  cases  in  which  it  is  practicable  to 
raise  the  money  required  for  the  concrete  construction,  excepting  only 
that  creosoted  wooden  blocks  on  a  reinforced  concrete  base  are  permis- 
sible on  account  of  being  almost  fireproof,  or  at  any  rate  very  slow-burning. 

An  exception  might  be  made  for  the  movable  span  in  a  bascule  bridge 
because  the  tipping  of  the  floor  to  a  vertical,  or  nearly  vertical,  position 
is  somewhat  objectionable,  although  it  is  not  impracticable  to  design  a 
concrete  floor  with  a  concrete  pavement  thereon  in  such  a  manner  as  to 
withstand  effectively  the  said  tipping.  In  case  the  timber  floor  be  adopted, 
it  would  be  necessary  to  take  the  utmost  precaution  against  injury  by  fire. 

Pavings  for  Roadways 

The  type  of  paving  to  adopt  depends  upon  whether  any  timber  is 
to  be  used  in  the  deck.     Planks  make  the  cheapest  kind  of  flooring,  but 


188  ECONOMICS   OF   BRIDGEWOKK  Chapter  XXI 

they  afford  a  poor  riding  surface  and  are  short-lived.  Transverse  planks 
are  objectionable  on  account  of  rough  riding,  and  diagonal  ones  are  better 
for  high-speed  traffic,  although  they  splinter  and  are  primarily  somewhat 
more  expensive — due  to  a  waste  in  cutting  them  to  proper  lengths.  Longi- 
tudinal planks  afford  the  easiest-riding,  but  they  do  not  wear  at  all  uniformly 
because  of  the  tendency  of  the  travel  to  run  in  certain  lines. 

Planks  can  be  either  untreated  or  creosoted.  Creosoting  delays  the 
process  of  decay  but  lowers  the  resistance  to  abrasion;  hence,  for  the 
wearing  floor,  untreated  planks  are  the  more  economical.  A  hard- 
wood tunber  that  does  not  warp  or  twist  excessively  is  the  best  for  the  said 
wearing  floor.  A  double-plank  floor  with  the  lower  laj^er  creosoted  and 
the  upper  layer  placed  diagonally  is  ultimately  the  most  economical  of  all 
plank  floors. 

With  the  creosoted  planks  it  is  practicable  to  use  a  pavement  of  cre- 
osoted pine  blocks,  but  the  combination  is  very  inflammable,  and  hence, 
is  not  truly  economic.  A  similar  pavement  can  be  used  to  advantage  for 
bascule  spans  by  adopting  instead  of  the  blocks  maple  planks  on  edge 
bolted  into  groups  and  attached  firmly  to  the  steelwork. 

With  a  concrete  base  any  desired  type  of  paving  can  be  employed — 
wood  blocks,  brick,  asphalt,  bitulithic  concrete  or  any  other  kind  of 
bituminous  paving,  plain  concrete,  or  granitoid.  Wood  block  is  the 
most  expensive  as  far  as  first  cost  is  concerned,  but  it  makes  a  much  better 
showing  in  the  comparison  when  maintenance  and  renewal  are  considered. 
Brick  per  se  is  less  expensive,  but  it  is  heavy  and,  in  consequence,  requires 
more  metal  to  carry  it.  This  is  not  a  serious  handicap  on  short-span 
bridges,  but  on  long-span  ones  it  is  almost  prohibitory. 

Asphalt  and  bituminous  pavements  in  general  are  good;  and  usually 
they  are  no  heavier  than  the  wooden-block  ones.  Unfortunately,  they 
require  an  extensive  plant  to  lay  them;  and,  as  the  total  area  of  paved 
surface  on  most  bridges  is  comparatively  small,  the  charge  per  square  yard 
for  use  of  plant  will  be  excessive,  unless  there  be  a  nearby  plant  available. 
To  adopt  an  asphalt  or  bitulithic  paving  on  a  bridge  in  a  small  town  is,  for 
that  reason,  rarely  economic  practice.  This  difficulty,  however,  can  be 
overcome  by  adopting  an  asphalt  block  pavement,  which  requires  no 
plant  for  its  construction. 

A  concrete  wearing-surface  in  many  cases  is  both  satisfactory  and  com- 
paratively inexpensive,  for  it  requires  no  special  plant  to  lay  it;  neverthe- 
less an  extra  hard  and  durable  aggregate  is  obligatory,  and  the  concrete 
must  be  very  carefully  mixed,  placed,  and  finished,  and  must  be  kept 
properly  wet  while  curing,  especially  in  hot,  dry  weather.  Unless  these 
prectautions  be  observed,  the  concrete  pavement  will  not  prove  economic 
b(H'ause  of  short  life  and  the  expense  of  repairs  and  replacement.  It  will 
b(>  found  advisable  to  design  with  an  allowance  in  dead  load  for  an  extra 
two  inches  of  concr(>te,  so  that  a  thick(M-  W(vu'iiig  surface  may  b(^  ]Mit  on,  if 
ever  desired,  without  overloading  the  floor-syst(un  or  the  trusses. 


ECONOMICS   or   DECKS   AND    FLOOR-SYSTEMS  189 

Sidewalks 

Sidewalks  are  usually  reinforced  slabs  of  granitoid  or  specially-hard 
concrete,  or  else  untreated  planks.  The  latter  are  the  cheapest,  even 
when  the  cost  of  maintenance  is  considered,  for  they  last  fairly  well; 
but,  like  all  other  timberwork,  they  are  subject  to  destruction  by  fire, 
involving  also  injury  to  the  metallic  portion  of  the  structure. 

Sub-Paving  or  Base 

As  previously  stated,  the  reinforced-concrete  slab  makes  the  best  and 
most  economic  base  for  pavement.  The  reinforcing  must  be  arranged  to 
suit  the  steel  floor-system,  which  will  be  described  later.  A  timber  base, 
either  plain  or  creosoted  is  not  truly  economic  construction  because  of  the 
fire  risk,  nevertheless  it  is  frequently  used  because  of  limited  funds,  or  for 
lack  of  appreciation  of  true  economy  in  design.  Comparing  creosoted  and 
plain  planking,  the  former  is  more  expensive  and  heavier,  but  the  plain 
plank  as  a  base  rots  so  rapidly  that  its  use  is  uneconomic.  Modern  con- 
centrated loads  require  that  the  distances  between  supports  for  the  planks 
be  small — say  two  feet  for  3-inch  planks  and  two  and  a  half  feet  for  4-inch 
ones.  The  former  thickness  is  totally  unfit  to  support  heavy  traffic,  espe- 
cially after  either  abrasion  or  decay  has  started.  With  the  live  loads 
adopted  in  the  standard  bridge-specifications  of  today,  timber  joists  .or 
stringers  are  not  truly  economic;  for  very  heavy  members  would  be 
required  for  panels  of  any  length,  even  down  to  the  shortest  ever  likely  to 
be  considered.  The  cheapest  timber  floor  is  obtained  by  plank  carried 
on  ties  supported  by  widely-spaced  steel  stringers.  Common  practice, 
however,  spaces  the  stringers  closer  and  puts  nailing-strips  thereon. 
This  increases  materially  the  cost  of  the  stringers. 

Curbs 

The  best  kind  of  curb  to  adopt  depends  essentially  upon  the  style  of 
deck.  With  a  concrete  deck  or  a  pavement  on  a  reinforced  concrete  base, 
a  concrete  curb  properly  faced  with  a  steel  angle  is  the  appropriate  con- 
struction; but  for  timber  decks,  wooden  guards  are  the  proper  thing. 
True  economj^  demands  that  the  drainage  of  the  deck  be  correctly  taken 
care  of,  either  by  openings  beneath  the  curbs  or  by  an  effective  grade  on 
the  roadway. 

Waterprooji'nn 

When  the  steelwork  is  encased  in  concrete,  or  when  no  dripping  of 
water  on  the  space  below  the  deck  is  allowable,  it  becomes  necessary  to 
provide  waterproofing  between  the  paving  and  the  sub-base.  The  mem- 
brane type  of  waterproofing,  previously  described  for  railroad  bridges,  is 
the  best  and  most  economical. 


190  ECONOMICS   OF   BRIDGEWORK  Chapter  XXI 


Handrails 

Handrails  are  made  of  concrete,  structural  steel,  gaspipe,  or  timber. 
The  concrete  rails  are  the  best  looking,  but  are  also  the  most  expensive. 
Contrary  to  the  general  ideas -of  engineers,  they  wiU  require  repairs  from 
time  to  time,  in  order  to  replace  chips  broken  off  from  the  sharp  edges  of 
columns  by  blows,  or,  by  spaUing  in  the  case  of  concrete  placed  in  cold 
weather  and  not  thoroughly  protected  against  freezing.  • 

Steel  handrails  are  expensive,  when  substantial;  and  they  require  paint- 
ing from  time  to  time. 

Gas-pipe  handrails  are  flimsy  in  appearance  and  ineffective  besides. 

Timber  handrails  are  the  cheapest,  but  like  all  other  timber  construc- 
tion in  bridges  they  are  objectionable  because  of  fire — besides,  the  ordinary 
ones  are  inherently  ugly. 

Electric-Railway  Tracks 

With  timber  decks  the  problem  of  caring  for  the  electric-railwa}'^  tracks 
is  a  simple  one,  but  with  a  permanent  deck  it  is  somewhat  difficult,  involv- 
ing, as  it  does,  some  economic  considerations.  In  the  first  place,  the  rails 
must  be  of  a  height  to  suit  the  pavement  adopted,  and  their  heads  must  be 
flush  with  the  top  thereof.  Next,  the  best  method  of  support  is  a  knotty 
point  to  solve.  For  a  concrete  deck  there  can  be  employed  timber  ties 
surrounded  with  either  ballast  or  concrete,  or  steel  ties  embedded  in  con- 
crete, or  steel  ties  embedded  in  the  reinforced-concrete  slab  and  resting 
directly  on  the  steel  stringers,  or  steel  rail-chairs  supported  in  a  similar 
manner.  When  the  roadway  and  the  railway  are  separated  so  that  the 
two  kinds  of  traffic  cannot  mingle,  any  of  the  types  of  floor  previously 
described  for  steam  railways  can  be  used.  The  wooden  ties  are  generally 
the  least  expensive  type  of  track,  and  steel  ties  in  a  concrete  base  are  costly. 
Steel  ties  in  the  reinforcing  slab  and  resting  directh^  on  the  steel  stringers 
make  good  construction,  especially  for  long-span  bridges.  Steel  chairs 
are  cheaper  and  fairly  good,  but  they  do  not  ensure  a  perfect  spacing  of  the 
rails.  Wooden  ties  in  ballast  are  cheap  per  se,  but  the  construction  is 
heavy,  and,  therefore,  expensive  for  all  but  very  short  spans. 

Floor-Systems 

The  arrangement  of  the  floor-system,  i.e.,  stringers,  joists,  floor-beams, 
and  cross-girders,  with  their  bracing,  depends  upon  both  the  t>'i)c  of  deck 
adopted  and  the  kind  of  span  employed. 

In  I-beam  spans  there  is  no  need  for  a  floor-system,  because  they  are  so 
short  that  a  concrete  deck  is  all  they  require;  and  its  extra  weight,  as  com- 
pared with  that  of  the  open  dock  of  timber  ties,  does  not  add  appreciably  to 
the  cost,  because  of  the  large  ratio  in  any  case  of  live  load  to  dead  load. 
The  o(!onomical  spacing  of  the  I-beams  varies  from  six  to  ten  feet,  increasing 
gradually  with  the  span  length.     The  undcM'-ckvirance,  however,  may  be 


ECONOMICS   OF   DECKS   AND   FLOOR-SYSTEMS  191 

limited,  requiring  close  spacing,  so  as  to  permit  the  adoption  of  shallower 
sections  than  the  economic  ones.  The  beams  are  frequently  encased  in 
concrete  in  order  to  protect  the  metal  from  the  fumes  of  locomotives  passing 
below.  If  a  timber  deck  should  be  adopted  with  planks  resting  either 
directly  on  the  stringers  or  on  nailing-shims  bolted  thereto,  the  spacing 
should  be  some  two  and  a  half  feet,  more  or  less,  depending  upon  the  size 
of  the  concentrated  wheel-loading;  but,  if  the  planks  are  carried  on  wooden 
ties,  the  spacing  may  be  made  about  five  feet. 

In  deck,  plate-girder  spans  also,  the  floor-system  can  sometimes  be 
omitted,  especially  in  short  spans,  with  either  concrete  deck  or  planks  on 
ties;  but  in  long  spans  of  this  type  the  steel  floor-system  will  generally  be 
found  more  economical.  The  limiting  span-length  for  omission  of  floor- 
system  is  sixty  or  seventy  feet,  as  far  as  the  economics  of  the  superstructure 
alone  are  concerned ;  but  such  extreme  lengths  may  increase  too  greatly  the 
cost  of  the  supporting  parts.  For  instance,  with  only  two  lines  of  main 
girders  and  a  floor-system  there  will  be  required  only  two  columns  per  bent 
and  two  pedestals  to  support  them;  whereas  with  several  lines  of  girders 
there  must  be  several  columns  and  pedestals  per  bent,  or  else  a  heavy  cross- 
girder  or  a  continuous  concrete  pier,  either  of  which  is  more  expensive  than 
a  pair  of  columns  with  their  pedestals  and  bracing.  If  for  any  reason  it  be 
decided  to  use  continuous  shafts  in  the  piers,  there  may  be  no  extra  expense 
due  to  supporting  several  lines  of  girders ;  in  fact,  there  may  be  a  reduction 
in  cost,  because  it  might  be  possible  to  employ  narrower  piers  or  seats. 

In  deck,  plate-girder  spans  with  floor-systems  it  is  economic  to  use  only 
two  lines  of  main  girders  up  to  a  fifty-foot  total  width  of  deck  or  in  some 
cases  even  sixty  feet.  The  girders  for  economy  should  generally  be  placed 
at  the  quarter  widths,  so  as  to  obtain,  in  both  substructure  and  super- 
structure, the  full  economic  benefit  of  the  cantilevering.  In  narrow  struc- 
tures the  spacing  should  be  proportionately  greater  for  the  sake  of  rigidity 
and  stability.  With  three  lines  of  main  girders,  the  spacing  should  be 
about  one-third  of  the  total  width  of  che  deck. 

The  standard  floor-system  in  deck,  plate-girder  construction  has 
stringers  carried  on  floor-beams.  The  portions  of  the  latter  outside  of 
the  outer  girders  are  cantilever  beams  with  a  strap-plate  over  the  top  of 
the  main  girder  and  some  kind  of  properly  designed  detail  below  to  carry 
the  compression  from  the  bottom  flange  of  the  cantilever  to  the  bottom 
flange  of  the  floor-beam.  The  stringers  are  generally  rolled  I-beams  and 
the  cross-girders  built  beams,  although  occasionally  it  will  be  found 
economic  to  employ  a  deep  rolled-I-beam.  With  planks  resting  on  stringers, 
either  directly  or  by  interposed  naihng  strips,  the  stringer  spacing  will, 
of  course,  be  determined  by  the  size  of  the  specified  concentrated  live 
loads  and  the  assumed  thickness  and  kind  of  material  of  plank.  It  is 
generally  about  two  feet  for  three-inch  plank  and  two  and  a  half  feet  for 
four-inch  plank.  Closer  spacings  than  these  involve  an  extravagant 
amount  of  metal  for  stringers. 


192  ECONOMICS   OF  BEIDGEWORK  Chapter  XXI 

With  planks  resting  on  ties,  a  spacing  of  five  feet,  or  even  more,  can 
be  used,  depending,  of  course,  on  the  size  and  strength  of  tie  and  the 
assumed  concentrated  live  load.  This  wide  spacing  reduces  materially  the 
weight  of  metal  in  the  stringers,  thus  saving  more  than  enough  to  com- 
pensate for  the  cost  of  the  ties. 

With  a  concrete  deck  it  is  economical  to  space  the  stringers  from  six 
to  ten  feet,  there  being  very  little  difference  in  total  cost  for  variations 
between  this  range.  It  is  better,  as  a  rule,  to  adopt  the  smaller  limit  so 
as  to  reduce  the  cost  of  the  slab-forms.  The  economic  panel-length  is 
small,  running  from  ten  or  twelve  feet  for  a  twenty-foot  spacing  of  main 
girders  to  fifteen  feet  for  a  thirty-foot  spacing,  and  to  eighteen  feet  for  a 
fifty-foot  spacing.  It  is  specially  short  for  closely-spaced  stringers  with 
plank  floor.  In  general  it  may  be  said  that  the  greatest  economy  obtains 
when  one  of  the  standard  beams  just  barely  figures  as  a  stringer.  For 
instance,  if  in  choosing  between  a  six-foot  and  a  seven-foot  stringer-spacing, 
the  20"  65  lb.  I  just  figures  for  the  latter  and  must  also  be  used  for  the 
former  because  the  18"  60  lb.  I  is  not  strong  enough,  it  will  be  found 
economical  to  adopt  the  greater  spacing.  On  the  other  hand,  if  the  18" 
55  lb.  I  just  figures  for  the  six-foot  spacing,  and  the  20"  65  lb.  I  is  required 
for  the  seven-foot  spacing,  the  former  will  prove  the  more  economic. 

The  question  of  extra  metal  in  girders  or  trusses  to  carry  heavier  slabs 
is  not  important  with  short  spans,  but  is  very  much  so  with  long  spans. 

With  concrete  deck  on  plate-girder  spans  it  will  sometimes  be  found 
cheaper  to  use  no  stringers,  but  to  employ  -rather-closely-spaced  cross- 
girders  on  which  the  slab  rests  directly.  The  economic  spacing  of  these 
girders  figures  out  twelve  feet  or  more,  so  far  as  quantities  of  materials 
are  concerned;  but  it  is  better  to  use  ten  feet  or  even  less,  because  the 
supporting  of  the  slab-forms  for  the  long  panels  is  expensive.  This  type  of 
floor  is  specially  adapted  to  through,  plate-girder  spans  and  will  be  dis- 
cussed further  in  connection  therewith.  It  does  not  save  quite  so  much 
with  deck  plate-girders,  as  the  girders  themselves  form  two  or  more  lines 
of  stringers;  hence  the  total  weight  of  stringer  metal  which  can  be  saved 
is  less  with  deck  plate-girders  than  with  through  plate-girders.  Again, 
an  outside  stringer  may,  in  any  case,  be  required  to  support  the  hand- 
railing. 

When  the  structure  carries  electric  railway  tracks,  a  stringer  must  be 
placed  under  each  rail.  The  addition  of  such  stringers  would  practically 
eliminate  the  saving  above  discussed;  and,  therefore,  the  standard  type 
of  floor-system  with  stringers  and  floor-beams  should  be  employed. 

Sidewalk  slabs  should  be  carried  on  longitudinal  stringei-s,  even  if  the 
cross-girders  are  spaced  closely.  The  outside  stringer  should  generally 
be  a  channel  so  as  to  provide  a  flush  surface  for  the  attachment  of  the  hand- 
railing;  and  with  short  panels  the  inner  stringers  may  be  of  the  same  sec- 
tion. Vov  five-foot  walks  two  stringers  will  give  the  cheapest  construc- 
tion, the  curb  stringer  of  the  roadway  sometimes  being  utilized  as  one  of 


ECONOMICS   OF   DECKS   AND   FLOOR-SYSTEMS  193 

them.  For  eight-foot  or  ten-foot  sidewalks  three  stringers  are  economic. 
Sidewalks  on  deck,  plate-girder  bridges  reduce,  or  even  eliminate,  the 
economy  of  the  stringerless  type  of  floor-system. 

With  half-through,  plate-girder  spans,  the  positions  and  numbers  of 
girders  are  generally  fixed,  two  being  just  outside  of  the  curb-hnes;  but 
in  wide  roadways  it  is  economic  to  use  three  hues  of  girders,  although  the 
splitting  of  the  traffic  by  the  middle  girder  is  not  a  desirable  feature.  In 
the  case  of  a  very  shallow  floor,  though,  such  splitting  cannot  be  avoided. 

The  stringerless  type  of  floor-system  is  nearly  always  cheaper  in  half- 
through,  plate-girder,  spans  than  the  standard  type  with  its  stringers  and 
floor-beams.  With  electric-railway  tracks  the  advantage  is  smaller  than 
where  there  are  none.  With  no  such  tracks  the  saving  of  metal  amounts 
to  some  200  lbs.  per  lineal  foot  of  span  for  a  structure  of  any  ordinary 
width;  and  the  excess  cost  of  the  thicker  slab  is  small.  Again,  the  stringer- 
less type  is  shallower  than  the  other — which  is  often  very  important.  By 
spacing  the  beams  closely  a  very  shallow  floor  can  be  obtained  at  moderate 
cost;  but  too  shallow  sections  are  not  desirable,  as  they  do  not  afford 
sufficient  lateral  support  for  the  top  flanges  of  the  main  girders. 

The  floor-systems  of  half -through,  plate-girder  bridges  very  often  must 
be  encased  in  concrete.  This  is  to  the  advantage  of  the  stringerless  type, 
which  has  smaller  area  to  cover  and  involves  more  simple  work. 

When  a  concrete  slab  is  employed,  it  should  be  carried  over  to  the  webs 
of  the  girders  and  supported  on  shelf  angles.  If  the  floor  is  encased,  the 
detail  at  the  girder  web  needs  careful  attention,  in  order  to  prevent  water 
from  entering  and  thus  causing  rusting  of  metal  and  splitting  off  of  encase- 
ment. 

Sidewalks  on  half- through,  plate-girder  spans  are  carried  on  cantilever 
brackets,  but  outer  steel  stringers  will  be  needed.  The  inner  edge  is 
supported  on  a  shelf  angle.  A  close  spacing  of  these  brackets  is  advan- 
tageous, as  generally  there  is  difficulty  in  properly  taking  care  of  large 
top-flange  tension. 

With  truss  spans,  the  standard  floor-system  of  stringers  and  floor-beams 
is  nearly  always  adopted,  because  it  would  usually  be  uneconomic  to  sup- 
port the  cross-girders  by  the  chords  between  panel  points.  As  previously 
indicated,  the  economic  panel  length  for  the  floor-system  per  se  is  from 
fifteen  to  seventeen  feet,  which  is  too  short  for  the  economics  of  the  trusses, 
hence  longer  panels  than  that  limit  generally  have  to  be  adopted.  For 
a  bridge  of  practically  any  width  of  roadway,  the  metal  in  the  floor-system 
with  25-foot  panels  weighs  about  70  pounds  per  lineal  foot  more  than  that 
required  for  the  economic  panel  length,  and  for  30-foot  panels  about  150 
pounds  per  lineal  foot  more.  Divided  panels  in  spans  of  moderate  length 
permit  the  use  of  the  economic  panel  length,  but  the  secondary  truss- 
members  increase  the  weight  of  metal  in  trusses  enough,  or  more  than 
enough,  to  offset  the  saving  in  the  floor-system.  With  long  spans,  how- 
ever, this  uneconomic  feature  disappears. 


194  ECONOMICS   OF   BRIDGEWORK  Chapter  XXI 

In  timber  decks  the  economic  stringer  spacing  is  about  the  same  as  it 
is  in  plate-girder  spans;  and  in  concrete  decks  it  is  five  or  six  feet  for  spans 
of  200  feet  or  under,  and  less  for  longer  spans.  For  instance,  in  spans  of 
400  feet  with  25-foot  panels  it  is  four  feet,  and  with  35-foot  panels  it  is  four 
and  a  half  feet. 

The  stringerless  type  of  floor  system  with  concrete  deck  for  very  short 
panels — say  12  feet — shows  the  same  economy  in  truss  spans  as  it  does  in 
haK-through,  plate-girder  spans.  With  truss-spans  of  moderate  length, 
the  panels  are  so  long  that  the  chords  would  have  to  be  built  as  girders  in 
order  to  carry  cross-girders  between  panel  points.  The  floor-system  itseK, 
as  compared  with  that  of  the  stringer  type,  when  the  panels  are  25  or  30 
feet  long  may  show  for  standard  deck-widths  a  saving  of  from  250  lbs.  to 
350  lbs.,  per  lineal  foot,  while  the  extra  metal  in  the  chords  required  to 
make  them  serve  as  girders  would  amount  to  250  or  300  lbs.;  besides 
which  there  must  be  taken  into  consideration  the  increase  in  weight  of 
truss-metal  due  to  the  augmented  dead  load  by  reason  of  the  thicker  slab. 
On  this  account  the  stringer  type  wiU  nearly  always  be  found  cheaper, 
especially  when  electric  railways  are  carried.  With  encasement  there 
may  be  an  economic  advantage  in  the  stringerless  type,  especiallj'  if  a 
very  shallow  floor  be  called  for.  With  extremely  long  panels  it  will  be 
found  cheaper  to  use  stringers  close  to  the  trusses  rather  than  to  stiffen 
the  chords  of  the  latter  enough  to  make  them  able  properly  to  carry  the 
transverse  loading. 

For  very  long  spans  with  concrete  slabs  it  is  desirable  to  reduce  the 
weight  of  deck  to  a  minimum.  In  such  cases  it  will  be  most  economic  to 
support  the  slab  on  closely-spaced  cross-beams  carried  on  stringers  rather 
widely  spaced — say  10  or  12  feet  centers.  Considering  both  the  weight 
of  metal  in  the  floor-system  and  that  in  the  trusses,  it  is  found  that  the 
economic  spacing  of  the  small  beams  is  about  three  feet.  Comparing  this 
with  the  ordinary  type  having  stringers  spaced  four  and  a  half  or  five 
feet,  it  will  be  found  that  the  metal  in  the  cross-beam  type  weighs  about 
three  pounds  more  per  square  foot  for  25-foot  panels  and  about  one  pound 
more  per  square  foot  for  35-foot  panels,  while  the  slab  weighs  eight 
pounds  per  square  foot  less.  The  total  deck,  therefore,  weighs  some  five 
pounds  per  square  foot  less  for  25-foot  panels  and  seven  pounds  per 
square  foot  less  for  35-foot  panels.  Considering  the  extra  weight  of 
truss-metal  needed  to  support  this  excess  of  dead  load,  and  remembering 
that  the  pound  cost  for  the  cross  beams  is  a  little  less  than  that  for  the 
remainder  of  the  floor-system,  it  has  been  figured  that  the  cross-beam 
type  is  cheaper  with  35-foot  panels  for  spans  in  excess  of  200  feet, 
cheaper  with  30-foot  panels  for  spans  of  350  feet,  and  cheaper  with  25-foot 
panels  for  spans  of  600  feet.  Evidently,  therefore,  there  is  no  economy 
in  adopting  this  type  for  spans  shortcM-  than  250  or  300  feet;  but  for  all 
long  spans  it  is  quite  economical. 

This  type  of  floor  affords  a  good  support  for  the  rails,  which  must, 


ECONOMICS   OF   DECKS   AND   TLOOR-SYSTEMS  195 

however,  be  made  quite  deep.  The  reinforced  slab  must  be  cut  back  from 
the  rail  in  order  to  permit  of  the  latter  being  removed.  This  detail  requires 
careful  watching. 

Sidewalks  on  through-truss  bridges  are  usually  placed  outside  of  the 
trusses  and  carried  on  longitudinal  stringers  supported  by  cantilever 
brackets. 

In  very-long-span  bridges,  such  as  cantilever  or  suspension  structures, 
the  matter  of  economy  from  deck  and  floor-system  should  be  very  closely 
studied,  in  order  to  eliminate  every  unnecessary  pound  of  dead  load. 
Preliminary  designs  should  be  made  for  various  types  and  for  different 
spacings  of  beams  and  stringers,  in  order  to  determine  the  most  economic 
arrangement.  The  question  of  total  weight  of  deck  may  be  far  more 
important  for  such  long-span  structures  than  the  total  weight  of  metal 
in  the  floor.  Timber  decks,  of  course,  will  be  much  cheaper  than  concrete 
decks;  and  the  decision  between  the  two  types  must  be  made  by  judgment, 
considering  the  nature  of  the  traffic,  the  money  available,  the  possible 
revenues,  the  first  cost,  the  cost  of  maintenance,  and  especially  the  danger 
from  fire.  In  general  it  may  be  said  that  the  concrete  deck  should  be 
adopted  if  sufficient  money  can  be  secured,  and,  for  a  toll  bridge,  if  the 
estimated  revenue  justifies  the  expenditure. 

There  is  a  Hght  type  of  floor  recommended  for  long  spans  by  Edward 
A.  Byrne,  Esq.,  Member  American  Society  Civil  Engineers,  Chief  Engineer 
of  the  Department  of  Plant  and  Structures  of  the  City  of  New  York.  It  ' 
consists  of  stiffened  buckle  plate,  having  the  buckle  down,  covered  with 
plain  concrete,  and  supporting  a  thin  block  pavement.  Concerning  this 
type  Mr.  Byrne  on  June  8,  1920,  wrote  the  author  as  follows : 

Where  buckle  plates  are  used  to  support  the  roadway  pavement  the  following 
detail  of  construction  is  suggested.  The  ends  of  all  buckle  plates  should  rest  on  supports 
and  be  properly  spliced.  The  fillets  of  the  buckle  plates  should  be  reinforced  by  angles 
— 3"X3"X|"  angles  have  proven  effective  in  buckle  plates  supported  on  stringers  five 
feet  on  centers.  The  plates  should  be  laid  with  the  buckle  down  and  filled  with  Port- 
land cement  concrete  to  a  depth  of  at  least  three  inches  above  the  top  of  the  plate. 
Longitudinal  angles,  3"X3"Xf",  should  be  riveted  to  the  buckle  plates  along  the  line 
of  the  supporting  stringers  to  restrain  the  concrete  foundation  and  act  as  a  template  for 
laying  the  concrete.  Each  buckle  plate  should  have  a  drain  hole;  and  a  hole  in  the 
concrete,  extending  from  the  top  thereof  to  the  buckle  plate,  should  be  provided.  On 
top  of  the  concrete  foundation  a  wood  block  pavement,  three  inches  in  depth,  should  be 
laid  without  any  cushion,  sand  to  be  spread  over  the  pavement  and  brushed  into  the 
joints.  The  Portland  cement  concrete  should  be  one  part  cement,  two  parts  sand,  and 
four  parts  broken  stone  or  gravel — the  top  to  be  rubbed  to  a  smooth  finish.  .  .  . 

It  is  highly  important  that,  in  using  a  buckle  plate  floor,  all  deflections  of  plates  be 
eliminated,  otherwise  the  concrete  foundation  will  crack  and  disintegrate. 

Tests  made  by  Mr.  Byrne  on  the  floor  of  the  Queensboro  Bridge,  where 
the  stringers  were  spaced  five  feet  on  centers  and  where  the  buckles  were 
about  four  feet  long,  showed  deflections  of  buckle  plates  as  great  as  three- 
eighths  of  an  inch  before  the  stiffening  angles  were  attached,  but  no 
appreciable  amount  after  they  were  put  on. 


196 


ECONOMICS   OF   BRIDGEWORK 


Chaptek  XXI 


The  cost  of  the  pavement-support  -per  se  is  about  twice  as  great  for  the 
buckle-plate  type  as  for  the  orchnary  type  with  reinforced-concrete  slab, 
0        100      200       300       400       300       600       700       dOO      POO      WOO 


200      300       400       300       600       700       600       $00      1000    ■ 
Span  leoqfd  /o  feef 

Ficj.  2lr;.     Diugnim  of  Iruiretiw!  in  Wcif^hl,  of  Metal  for  Each  Excess  Pound  of  Extrane- 
ous, Uiiiforinly-l)is(ril)ul(>(l  Tioad  in  Siniijle-Truss  Spans. 

the  (li(TcM(Mic(>  ;il  cmrcnt  i)iiccs  of  nuitcrials  and  labor  being  about  eighty 
cents  pc;f'  s(ju:uc  loot  of  fkjor;   but  there  is  a  saving  effected  in  the  dead 


ECONOMICS   OF   DECKS   AND   FLOOR-SYSTEMS 


197 


load  by  the  former,  amounting  to  about  eighteen  pounds  per  square  foot. 
For  a  simple  truss  span  of  600  feet,  it  requires  about  0.58  lb.  of  steel   to 


m    600 


2000    2m   2m 

3.0 


1000        m        1400    ^  1600 
/©7^/6,  of  Ma/n  Opepi/?q  //?  fee/- 

Fig.  216.     Diagram  of  Increase  in  Weight  of  Metal  for  Each  Excess  Pound  of  Extrane- 
ous, Uniformly-Distributed  Load  in  Type-A-Cantilever  Bridges. 

carry  an  extra  pound  of  extraneous  load ;  hence,  for  such  a  span,  the  extra 
metal  to  support  the  eighteen  pounds  of  excess  dead  load  of  the  floor  would 


198  ECONOMICS   OF   BRIDGEWORK  Chapter  XXI 

be  about  ten  and  a  half  pounds,  which,  at  the  present  unit  prices  of  mate- 
rial and  labor,  are  worth  in  place  about  84  cents,  showing  that  to-day  for 
simple-truss  spans  exceeding  600  feet  in  length  it  would  be  economic  to 
adopt  the  buckle-plate  floor. 

As  this  economic  question  is  likely  to  arise  at  any  time,  and  as  its  solu- 
tion is  largely  dependent  upon  the  relative  unit  prices  of  concrete  and 
structural  steel  in  place,  the  author  has  prepared  the  diagrams  shown  in 
Figs.  21a  and  216,  which  indicate  for  simple-truss  and  cantilever  spans, 
respectively,  and  for  both  carbon  steel  and  nickel  steel,  the  amount  of 
extra  metal  that  will  be  required  to  support  one  excess  pound  of  extraneous 
load  uniformly  distributed. 

Just  as  the  MS.  of  this  book  was  about  to  go  to  press,  the  author's 
attention  was  called  to  a  Hght  aggregate  for  concrete,  termed  Haydite, 
being  named  after  its  discoverer,  Mr.  Stephen  Hayde,  a  well-known  citizen 
of  Kansas  City,  Mo.  He  claims  that  concrete  made  of  it  weighs  only  108 
lbs.  per  cubic  foot,  as  against  150  lbs.  per  cubic  foot  for  ordinary  1:2:4 
concrete  of  small  broken  stone  or  gravel,  and  that  the  hghter  concrete 
not  only  is  practically  impervious  to  water,  but  also  that  it  gives  some  25% 
greater  resistance  to  compression  than  its  heavier  competitor.  If  these 
claims  are  correct,  there  should  be  quite  a  demand  for  Haydite  for  the 
bases  of  highway-bridge  floors,  especially  as  the  extra  cost  of  the  aggregate 
is  moderate.  Mr.  Hayde  and  his  business  associates  contemplate  retaining 
the  author  to  make  a  thorough  investigation  of,  the  suitability  of  Haydite 
for  pavement  bases  in  bridge  construction  and  to  show  by  diagrams  and 
otherwise  the  economics  involved  thereby.  Until  some  engineer  of 
standing  tests  the  new  aggregate  and  vouches  in  print  for  its  characteristics, 
the  profession  will  have  to  take  the  discoverer's  claim  cum  grano  salts; 
nevertheless,  the  author  has  great  hope  of  its  being  proved  to  be  all  that  is 
claimed.  If  such  be  the  case,  its  use  will  result  in  a  real  boon  to  the  builders 
of  modern,  first-class,  highway  bridges,  especially  those  of  long  span. 


CHAPTER  XXII 

GENERAL  ECONOMICS   OF  DESIGNING  AND  DETAILING 

In  this  chapter  will  be  treated  only  the  salient  economic  features  of 
ordinary  designing  and  detailing,  because  to  attempt  to  do  more  would 
lengthen  this  portion  of  the  book  beyond  all  reason. 

In  all  cases  it  is  economic  to  choose  the  most  simple  types  of  structures 
and  details,  and  especially  those  that  lend  themselves  best  to  stress 
analysis. 

One  should  select  members  which  by  form  and  location  are  best  adapted 
to  resist  forces  economically  and  to  carry  stresses  by  shortest  routes.  For 
instance,  in  a  long-span  truss  with  parallel  chords,  shear  is  transferred 
entirely  by  the  web  members;  and  the  path  of  the  web  stresses  is  much 
shorter  by  the  divided-triangular  truss  than  by  the  Pratt  truss,  hence  the 
use  of  the  former  is  economical.  But  in  short-span  trusses  the  verticals 
are  nearly  all  of  minimum  section,  hence  there  is  but  Httle,  if  any,  difference 
in  the  economics  of  the  two  types.  Similarly,  with  polygonal  top  chords, 
the  shear  on  the  webs  being  comparatively  small,  there  is  not  much  to 
choose  between  the  said  two  types. 

In  riveted  tension  members  the  riveting  should  be  arranged  so  as  to 
reduce  to  a  minimum  the  number  of  rivet-holes  to  be  taken  out  of  a  section; 
but  if  the  number  assumed  be  too  small,  material  will  be  wasted  at  splices 
in  developing  the  net  section,  because  extra  holes  above  the  number  that 
would  normally  be  employed  cannot  be  used  at  joints  unless  extra  section  is 
first  developed  into  the  splice-plates  or  gussets.  Furthermore,  the  section 
will  very  Hkely  be  reduced  in  detaihng,  without  the  fact  being  noted. 
This  will  overstress  the  metal  at  such  sections. 

In  compression  members  the  metal  of  the  section  should  be  arranged  to 
secure  the  largest  practicable  radii  of  gyration  without  involving  the  use 
of  metal  that  by  its  thinness  would  transgress  the  rules  of  standard  speci- 
fications, viz.,  minimum  limits  of  one  thirty-second  of  unsupported  width 
for  webs,  and  one  fortieth  thereof  for  cover-plates.  It  is  economic  to 
employ  fairly  heavy  angles,  as  thereby  the  radii  of  gyration  are  increased 
and,  in  consequence,  also  the  strength  of  the  strut.  If  the  unbraced  length 
of  the  piece  is  greater  in  one  direction  than  in  the  other,  the  section  should 
be  so  arranged  that  the  values  of  the  ratios  of  length  to  radius  of  gyration 
are  approximately  equal.  For  instance,  in  the  case  of  intersecting  diago- 
nals of  lower  lateral  bracing,  the  unbraced  length  in  one  direction  is  twice 
as  great  as  that  in  the  other.     Then  for  2-angle  sections  unequal-legged 

199 


200  ECONOMICS   OF   BRIDGEWORK  Chapter  XXII 

angles  should  be  employed  with  the  longer  legs  vertical;  but  for  4-angle 
sections  it  is  economic  to  make  the  longer  legs  horizontal  and  connect  the 
shorter  legs  by  a  single  line  of  lacing  placed  between  them.  For  vevy  long 
struts  it  is  economic  to  employ  four  angles  in  box  section,  connected  by 
four  lines  of  lacing. 

In  Ught  bridges  the  posts  can  be  made  either  of  H  section  or  of  four 
angles  with  either  a  web  or  lacing  between,  rather  than  of  two  channels 
laced.  This  arrangement  saves  considerably  in  weight  of  details,  but  some 
of  that  saving  is  lost  because  of  the  greater  sectional  area  required  to  allow 
for  the  reduced  radii  of  gyration. 

For  compression  members  which  carry  shear,  there  should  be  one  or 
more  webs  in  planes  parallel  to  the  said  shear.  Such  webs  can  be  employed 
to  advantage  also  in  simple  struts  of  large  cross-section.  If  lacing  can  be 
omitted  thereby,  a  saving  of  metal  may  result.  On  the  other  hand,  the 
radius  of  gyration  may  be  reduced  by  using  such  diaphragms,  thus,  lowering 
the  unit  stresses. 

In  railway,  deck  plate-girders,  as  far  as  weight  of  metal  is  concerned,  it 
is  economical  to  use  cover  plates  for  top  flanges,  but  this  requires  rivets  and 
the  variable  dapping  of  the  ties.  Rivets  increase  the  work  of  placing  and 
maintaining  the  ties,  and  deep  dapping  is  undesirable.  The  best  railroad 
practice  forbids  the  use  of  rivets  through  the  upper  horizontal  legs  of  the 
flange  angles  of  stringers  when  timber  deck  is  employed. 

Batten  plates  for  large  compression  members  must  be  excessivety  thick, 
unless  they  be  properly  stiffened  by  angles;  and  it  will  generally  be  found 
less  expensive  to  adopt  thin  plates  and  stiffen  them.  Unless  considerable 
metal  be  saved  by  that  expedient,  however,  it  is  better  not  to  do  this, 
because  the  addition  of  stiffening  angles  increases  materially  the  amount 
and  cost  of  the  shopwork^ — besides  it  may  involve  some  difficulty  in  han- 
dhng  the  members. 

In  compression  members  consisting  of  two  built  or  rolled  channels,  it 
is  usually  economical  of  metal  to  turn  the  said  channels  in.  However,  this 
increases  the  cost  of  the  shop  work,  because  lacing-rivets  when  the  channels 
are  turned  in  usually  cannot  well  be  machine  driven. 

In  designing  a  built  chord  for  a  bridge,  the  sections  must  be  determined 
by  considering  all  panels  of  the  chord  simultaneously.  It  is  well  to  adopt 
as  few  differing  thicknesses  of  metal  as  practicable,  and  to  arrange  the 
various  sections  so  as  to  avoid,  to  as  great  an  extent  as  possible,  the  use 
of  filling  plates  at  the  splices.  In  field  splicing  the  loss  of  loose  filling 
plates  is  a  cause  of  serious  troul)le  and  expense;  hence  they  should  be 
avoided.  For  the  sake  of  simplicity,  it  is  frequently  best  to  waste  metal  in 
some  of  the  panels;  but  such  waste  should  always  be  reduced  to  a  mininunn. 
When  cover  plates  arc  employed,  it  is  advisable  to  avoid  changes  in  the 
location  of  the  center  of  gravity  of  the  section. 

In  detailing  onc^  should  always  endeavor  to  use  metal  to  best  advantage; 
and  the  strength  of  each  detail  or  connection  should  be  figured  whenever 


GENEKAL   ECONOMICS    OF   DESIGNING   AND    DETAILING  201 

this  is  practicable.  When  exact  analysis  is  impossible,  an  ample  amount 
of  metal  should  be  used  so  as  to  avoid  any  possible  weakness  due  to  such 
uncertainty;  but  this  does  not  mean  that  it  is  well  to  be  recklessly  extrava- 
gant of  metal  in  order  to  save  the  trouble  of  figuring  the  sti'ength. 

It  is  false  economy  of  the  worst  type  to  skimp  details;  because  the 
saving  in  metal  is  comparatively  small,  and  the  loss  of  strength  may  be 
very  great.  It  is  worse  than  useless  to  adopt  low  unit  stresses  for  the  main 
members  and  put  in  weak  details;  for  the  stress  sheet  then  gives  a  false 
sense  of  security.  It  would  be  much  better  to  have  strong  details  and  high 
working  stresses  in  the  main  members. 

Details  and  joints  frequently  defy  exact  analysis;  and  in  such  cases  the 
designer  should  not  fail  to  make  approximate  analyses  to  determine  the 
character  and  magnitude  of  stress  in  every  part  so  as  to  avoid  all  possibility 
of  the  existence  of  weak  spots.  It  is  not  unusual  to  see  metal  placed  at  a 
joint  where  it  could  not  possibly  do  any  good,  while  an  important  com- 
ponent part  of  a  member  is  left  unspliced.  A  ten  per  cent  error  in  strength 
on  the  side  of  danger  will  rarely  do  any  harm ;  but  the  complete  omission  of 
a  vital  part  of  a  detail  may  be  very  serious.  For  instance,  in  the  lateral 
systems  of  highway  bridges,  it  is  not  uncommon  to  see  a  diagonal  of  strong 
section  connected  by  details  so  flimsy  that  they  could  not  possibly  transmit 
one-quarter  of  the  stress  which  the  said  diagonal  is  capable  of  withstand- 
ing.    The  m'etal  in  such  a  lateral  system  is  nearly  all  wasted. 

As  an  important  matter  of  economy,  rusting  and  other  kinds  of  deterio- 
ration should  be  carefully  considered  when  making  designs.  It  is  very  un- 
economical to  use  parts  which  will  rust  out  or  wear  out  in  a  small  fraction 
of  the  possible  life  of  the  structure.  Repairs  are  not  only  expensive  'per  se, 
but  also  they  generally  interfere  seriously  with  the  traffic.  Some  mipor- 
tant  railroads  use  ys  ii^ch  or  even  ^  inch  as  the  minimum  thickness  of 
metal  in  steel  superstructures;  because  they  find  thin  metal  to  be  one  of  the 
most  fruitful  causes  of  replacement.  The  author,  however,  is  of  the  opin- 
ion that,  if  the  said  companies  were  to  adhere  to  the  f  inch  minimum 
thickness  and  keep  the  metal  always  properly  painted,  they  would  obtain 
more  satisfactory  results. 

All  parts  should  be  easily  accessible  to  the  paint  brush;  for  otherwise 
the  painters  wiU  fail  to  cover  some  metal  that  is  difficult  to  reach,  thus 
curtailing  the  fife  of  the  structure.  A  horizontal  plate  in  a  bottom  chord 
will  frequently  save  metal;  but  it  invites  rusting,  and  therefore  is  sure 
ultimately  to  prove  uneconomical. 

When  there  is  a  choice  of  plates  and  shapes  that  can  be  used  in  the  malce- 
up  of  a  member,  it  is  sometimes  practicable  to  economize  a  little  by  adopting 
the  most  inexpensive  ones;  but  too  often  it  will  be  found  that  the  more 
expensive  shapes  are  also  the  ones  which  are  the  more  appropriate  and 
serviceable. 


CHAPTER  XXIII 

ECONOMICS   IN   DESIGN    FOR    SHOP    CONSIDERATIONS 

While  the  consulting  bridge  engineers  of  America  do  not  yet  agree 
entirely  with  the  engineers  of  the  bridge  manufacturing  companies  concern- 
ing all  points  of  design,  the  ideas  of  both  have  of  late  been  gradually  getting 
closer  together.  The  differences  of  opinion  are  generally  in  the  line  of 
economics,  the  shopmen  desiring  to  cheapen  work  in  ways  of  which  the 
consulting  engineers  disapprove. 

Designs  should  be  made  so  as  to  afford  the  bridge  shops  every  facility 
possible  for  using  their  machinery  to  advantage.  For  instance,  details 
should  be  arranged  for  multiple-punch  spacing,  and  to  suit  the  requirements 
for  bending,  machining,  and  the  various  other  operations  which  are  gov- 
erned by  the  shop  equipment. 

One  great  bone  of  contention  in  times  past  was  the  matter  of  sub-punch- 
ing and  reaming  as  against  punching  full-size  and  running  a  loose  reamer 
through  the  holes  in  the  assembled  component  parts,  so  as  to  ensure  the 
possibility  of  the  passage  of  the  hot  rivets.  Even  today  much  work  is  done 
by  the  latter  method,  but  it  is  generally  confined  to  parts  of  so-called  minor 
importance.  The  object  of  sub-punching  and  reaming  is  two-fold:  first, 
to  make  the  holes  in  the  component  parts  match  properly  after  the  passage 
through  them  of  rigid-drill  reamers,  and,  second,  to  cut  away  the  metal 
around  the  peripheries  of  the  holes  which  was  injured  by  the  brutal  process 
of  punching.  The  author,  if  he  could  always  have  his  way  in  this  matter, 
would  bar  entirely  the  punching  of  holes  full-size;  and  he  believes  the  day 
is  coming  when  even  the  sub-punching  and  reaming  will  be  prohil^ited  by 
adopting  the  method  of  solid  drilling.  He  has  asked  some  of  the  })rominent 
bridge  manufacturers  how  much  extra  it  would  cost  to  employ  the  latter 
method,  and  has  been  told  that,  if  the  shops  were  propo-ly  outfitted  for  the 
work,  the  excess  cost  as  compared  with  sub-punching  and  reaming  would  be 
practically  nil.  For  nickel  steel  and  other  high-alloy  steels  solid  drilling 
should  be  exclusively  employed. 

In  the  case  of  sheared  edges,  if  the  metal  near  the  shear  is  to  be  depended 
on  for  strength,  the  said  edges  should  be  planed,  but  otherwise  the  planing 
should  ])(\  omitted,  unless  the  raw  edges  would  be  too  much  in  evidence  to 
th(!  b(!hold(;r  of  the  finished  structure.  It  is  more  than  probable  that  the 
shearing  of  edges  is  just  as  destructive  as  the  punching;  for  the  brutality  of 
the  treatment  of  the  metal  in  the  two  cases  is  of  the  same  character  and 
apparently  of  the  same  severity. 

202 


ECONOMICS    IN    DESIGN    FOR    SHOP    CONSIDERATIONS  203 

While  it  is  undoubtedly  difficult  to  procure  a  tight  fit  for  stiffeners  on 
rolled  I-beams,  it  does  not  appear  to  the  author  safe  to  omit  them  at  the 
ends  of  railway  girders  that  are  supported  from  beneath,  or  even  from  those 
used  for  carrying  heavy  highway  loads  to  the  masonry,  because  the 
unsupported  webs  are  not  of  a  shape  satisfactorily  to  resist  severe 
pounding. 

Although  it  is  true  that  turning  the  flanges  of  channels  in  makes  the 
riveting  somewhat  more  difficult,  it  need  not  prevent  the  use  of  power 
riveters,  except  in  the  case  of  a  few  rivets;  while  it  facilitates  greatly  the 
detailing  by  bringing  all  the  webs  of  main  truss  members  in  the  same 
plane  for  the  attachment  of  the  gusset  plates.  Most  of  the  author's  riveted 
bridges  are  built  in  this  way. 

Again,  it  is  important  to  have  the  batten  plates  inside  of  the  gussets, 
and  to  carry  them  to  near  the  ends  of  the  members,  both  of  which  condi- 
tions the  turned-in  channels  permit.  Moreover,  they  generally  involve 
an  economy  of  weight  of  metal  for  lacing  and  battens.  But  one  of  the 
most  important  advantages  of  turned-in  channels  is  that  they  permit  the 
ends  of  the  floor-beams  to  fit  closely  to  the  bottom  chords  without  cutting 
either  the  chord  or  the  beam,  which  is  not  practicable  if  the  flanges  of  the 
bottom  chords  turn  out. 

In  viaduct  construction  some  manufacturers  use  their  influence  to  have 
the  girder-depth  the  same  from  end  to  end  of  structure,  which  is  uneconomic 
of  material,  because  the  tower  spans  and  the  intermediate  spans  are  nearly 
always  of  different  lengths,  which  arrangement  would  call  for  different 
depths  unless  metal  is  to  be  wasted.  The  manufacturers'  claim  has  appar- 
ently some  justification  if  the  tops  of  the  columns  are  cut  off  so  as  to  let 
the  main  girders  be  supported  directly  thereon;  but,  in  the  author's  prac- 
tice, the  columns  are  carried  up  to  the  level  of  the  deck,  and  both  the  longi- 
tudinal girders  and  the  tower  cross-girders  abut  into  them;  hence  there  is 
no  valid  objection  to  making  the  comparatively-short  longitudinal-girders 
over  the  towers  shallower  than  the  long,  intermediate  longitudinal-girders. 
This  layout  certainly  looks  much  better;  and  the  corner  brackets 
afford  an  excellent  connection  for  the  diagonals  of  the  longitudinal 
bracing. 

If  the  designing  of  details  be  left  to  the  manufacturers  of  the  metalwork, 
they  often  place  the  end  or  pedestal  pin  of  a  riveted-truss  span  below  the 
bottom  chord,  forgetting  that  the  thrust  of  a  braked  train,  acting  with  a 
lever  arm  equal  to  the  vertical  distance  between  the  center  of  the  chord 
and  the  center  of  the  pin,  produces  a  large  bending  moment  that  has  to 
be  resisted  by  the  stiffness  of  the  bottom  chord  and  that  of  the  inclined 
end  post. 

When  bridge  superstructures  are  let  to  the  manufacturers  by  the  lump 
sum  and  they  have  the  designing  to  do,  they  like  to  omit  the  end  floor  beams 
of  through  bridges,  substitute  instead  inexpensive  struts,  and  rest  the 
stringers  on  the  masonry;   but  the  author  beheves  that  invariably  end 


204  ECONOMICS    OF   BRIDGEWORK  Chapter  XXIII 

floor-beams  should  be  employed  and  be  riveted  to  the  end  posts  of  the 
trusses  so  as  to  make  the  lower  lateral  system  a  harmonious  whole;  and  it 
matters  not  if  the  end  posts  be  inchned. 

Manufacturers  are  willing  to  use  single  angles  in  tension,  but  this  is 
objectionable  because  of  the  violation  of  the  rules  of  symmetiy  and  the  con- 
sequent causing  of  secondaiy  stresses. 

A  mooted  point  in  designing  is  the  exact  location  of  top-chord  pins. 
The  author  believes  they  should  always  be  placed  either  on  or  a  very  little 
below  the  gravity  lines  of  the  sections,  for  it  takes  an  exceedingl3r  small 
eccentricity  to  produce  a  high  intensity  of  bending  stress  on  the  chord. 
It  is  not  right  to  assume  that  the  reverse  bending  moment  due  to  the  weight 
of  the  member  between  panel-points  will  entirely  counteract  the  bending 
moment  due  to  the  eccentricity;  because  the  form  taken  under  loading  by 
the  center  line  of  the  long  strut  will  be  a  waved  line  passing  through  the 
centers  of  the  chord  pins,  being  concave  upward  in  one  panel  and  convex 
upward  in  the  adjoining  one.  The  amount  to  lower  the  chord  pins  below 
the  centers  of  gravity  of  the  sections  is  to  be  determined  by  making  the 
compressive  intensity  due  to  eccentricity  equal  to  the  tensional  intensit}'' 
due  to  bending  from  weight  of  member.  In  any  case  this  adjustment  is  a 
matter  of  compromise  on  account  of  the  shifting  of  centers  of  gravit}^  from 
centers  of  figure  by  reason  of  the  variation  in  make-up  of  section  from  pangl 
to  panel,  the  amount  ordinarily  varying  from  zero  to  a  quarter  or  three- 
eighths  of  an  inch.  In  large  bridges,  of  course,  the  variation  will  be 
greater  than  this. 

Manufacturers  hke  to  use  cast  iron  in  bridges  on  account  of  its  com- 
parative cheapness  per  pound;  but  on  general  principles  the  author  tries 
to  bar  out  all  cast  iron  from  his  bridges,  fearing  that,  if  it  be  permitted  in 
one  place,  the  contractor  will  insist  upon  putting  it  into  another.  Cast 
iron  is  nearly  always  inferior  to  cast  steel  for  any  purpose. 

There  is  an  uneconomic  detail  which  is  too  often  employed  in  both 
trestles  and  elevated  railroads,  viz.,  the  insertion  of  a  heavj^  casting  between 
the  lower  end  of  a  column  and  the  masonry.  The  author  has  never  been 
able  to  i^erceive  the  philosophj^  of  this  detail;  for  it  involves  the  planing  of 
a  large  amount  of  extra  surface  as  well  as  a  considerable  increase  in  the 
weight  of  metal.  Moreover,  the  additional  surfaces  in  contact  do  not 
militate  towards  rigidity,  for  perfect  contact  is  not  always  attained.  The 
object  is  evidently  the  spreading  of  the  load  over  the  masonry;  but  this 
could  be  accomplished  just  as  effectively  and  at  less  cost  by  using  a  rolled 
base-plate  of  the  proper  size  and  carrying  the  load  to  it  from  the  colunui 
section  by  means  of  vertical  plates,  horizontal  connecting  angles,  and  verti- 
cal stiffening  angles.  The  necessity  for  giving  the  latter  a  tight  fit  at  tlieir 
lower  ends  i-ecjuires  some  troublesome  shojiwork,  but  the  additional  cost 
thei'(!of  will  not  offset  the  expense  of  the  extra  amount  of  planing  involved 
by  tlic  (iasting  detail. 

In  respect  to  the  general  and  detail  principles  of  the  economics  of  shop- 


ECONOMICS    IN    DESIGN    FOR    SHOP    CONSIDERATIONS  205 

work  advocated  by  the  highest  authorities  on  the  manufacture  of  structural 
steel  and  concurred  in  by  the  author,  the  following  may  be  stated.* 

Attention  should  be  paid  by  designers  to  the  different  pound  prices  for 
the  various  sections,  and  they  should  remember  that  these  variations  are 
lilvely  to  change  from  time  to  time.  For  instance,  all  angles  over  6"  and 
all  beams  over  15"  deep  cost  a  small  amount  above  the  base  price;  and  for 
large  plates  the  extras  increase  with  the  widths  by  a  rapidly  augmenting 
scale,  starting  generally  from  100"  with  a  trifling  amount  and  reaching  as 
much  as  one  cent  per  pound  extra  for  a  width  of  130".  It  is,  therefore, 
often  more  economic  to  adopt  the  shallower  of  two  widths  and  use  a  little 
more  metal,  especially  when  the  variation  of  an  inch  or  two  of  girder-depth 
would  change  the  pound  price  of  the  raw  material  in  the  web  plates  as 
much  as  a  quarter  of  a  cent.  Large  differences  have  existed  at  times 
during  the  past  few  years,  plates  sometimes  being  very  expensive  and 
almost  unprocurable. 

In  the  design  for  structural  work  for  all  purposes,  more  consideration 
should  be  given  by  the  designer  to  the  sections  which  are  employed.  Spe- 
cial material  should  be  avoided,  if  possible;  sections  varying  by  xe  inch 
should  be  so  combined  as  to  use  one  section  as  far  as  practicable;  and  spe- 
cial sections  in  small  quantities  should  be  eliminated  entirely.  Very  often 
the  delivery  on  the  contract  is  delayed  because  the  shop  has  to  wait  for  a 
small  quantity  of  a  special  section  which  is  not  rolled  on  time.  Compli- 
ance with  the  above  will  insure  better  deliveries  from  the  mill  and  quicker 
fabrication  in  the  shop ;  and  all  parties  concerned  will  be  benefited  thereby. 

When  ordering  plates,  the  designer  should  adhere  to  standard  dimen- 
sions as  far  as  possible.  This  can  always  be  done  in  the  case  of  lateral  and 
gusset  plates,  but  a  special  depth  may  be  necessary  at  times  for  the  webs  of 
stringers  or  girders.  Standard  widths  for  plates  are  7,  8,  9,  10,  11,  12,  13, 
14,  15,  16,  18,  20,  24,  30,  36,  and  48  inches. 

Eye-bars,  adjustable  members,  turnbuckles,  screw-threads,  segmental 
rollers,  devices,  upsets,  etc.,  should  be  designed  according  to  the  standards 
of  the  bridge  manufacturers,  because  quicker  deliveries  and  better  fabrica- 
tion are  obtained  by  the  use  of  standards. 

Designs  should  be  made  so  that  all  extra  or  unnecessary  operations  in 
the  shop  are  avoided.  This  should  apply  particularly  to  large  and  heavy 
members  and  to  small  members  used  in  large  nmnbers.  The  work  on  these 
pieces  should  be  kept  as  simple  as  possible.  When  there  is  an  extensive 
duplication  of  any  piece,  it  will  pay  in  its  designing  to  save  every  pound  of 
metal  that  can  legitimately  be  omitted. 

Reaming  to  templets  is  useless  unless  the  templets  can  be  set  from 
finished  surfaces,  as  in  chord  splices,  ends  of  stringers,  floor-beam  connec- 
tions, etc.     Reaming  of  laterals  to  templets  is  liable  to  do  more  harm 

*  The  data  for  most  of  the  remainder  of  this  chapter  were  furnished  to  the  author 
in  1915  for  Chapter  XVII  of  "Bridge  Engineering"  through  the  courtesy  of  Messrs. 
Paul  L.  Wolfel  and  Albert  F.  Reichmann. 


206  ECONOMICS   OF   BRIDGEWORK  Chapter  XXIII 

than  good,  as  no  finished  surfaces  are  available.  The  same  apphes  to  diag- 
onals in  trusswork.  While  in  a  punched  connection  a  few  holes  may  be 
slightly  out,  which  can  be  corrected  in  the  field,  if  a  connection  is  reamed 
to  templet  and  the  templet  is  not  properly  set,  all  holes  wiU  be  equally  out. 
Riveted  trusses  should  be  reamed  and  match-marked  in  the  maker's  shop 
when  assembled. 

In  aU  plate  girders  and  truss-bridge  stringers  the  lateral  system  should 
be  dropped  so  that  the  rivet  heads  thereof  will  clear  the  ties. 

Wherever  possible  in  heavy  work,  avoid,  in  the  construction  of  the 
chords  or  web  members,  side  plates  or  doubhng  up  of  the  web  plates.  It 
will  often  pay  to  use  heavier  web  plates  without  side  plates^  even  if  they 
have  to  be  drilled  from  the  solid.  If,  however,  webs  have  to  be  doubled 
up  or  side  plates  used,  the  stitch  rivets  made  necessary  by  this  construc- 
tion should  be  reduced  to  a  reasonable  amount.  If  a  plate  is  used  as  a 
cover  plate  in  a  chord,  it  is  good  practice  to  hmit  its  thickness  to  ^oth 
of  the  distance  between  rivets.  If  the  same  plate  were  used  as  a  side  plate 
in  a  chord,  in  most  designs  two  or  three  times  as  many  lines  of  rivets 
would  be  called  for  as  would  be  necessary  by  the  above  limits. 

It  is  cheaper  and  better  to  use  heavy  flange  angles  in  stringers  than 
lighter  angles  with  cover  plates,  even  if  the  said  angles  should  have  to  be 
drilled  from  the  solid. 

Beveled  cuts  are  to  be  avoided  whenever  possible,  especially  beveled  cuts 
for  angles  that  cannot  be  obtained  by  cutting  multiple  pieces  from  a  long 
piece;  also  beveled  cuts  in  all  beams  and  channels,  as  these  have  to  be  sawed. 

One  of  the  greatest  savings  in  recent  years  in  bridge  shops  has  been 
made  by  the  use  of  multiple  punches.  These  not  only  reduce  the  cost 
of  the  punching  proper,  but  also  save  the  cost  of  making  templets  and  the 
laying  out  of  the  material.  They  further  give  far  superior  work;  as  the 
effect  of  the  stretch  of  the  material  during  punching  on  the  accuracy  of 
the  work  is  eliminated,  if  these  multiple  punches  are  property  constructed. 
Their  use,  therefore,  should  be  encouraged  in  every  way.  In  order  to  do 
this,  it  is  necessary  to: 

(a)  Keep  all  rivets  in  line  longitudinally. 

(6)  Keep  as  many  rivets  in  line  transversely  as  possible  and  do  not  use 
any  more  combinations  of  rivets  transversely  than  necessary. 

(c)  Never  have  the  longitudinal  fines  of  rivets  less  than  21"  apart,  nor 
the  transverse  lines  less  than  1|". 

Do  not  crimp  stifTeners  if  it  can  be  helped,  especially  do  not  crimp 
stiffeners  of  short  lengths,  say  up  to  about  three  feet.  If  stiffencrs  are 
crimped  |"  or  more,  the  crimp  is  unsightly;  and  better  and  more  sightly 
work  win  be  ol^tained  by  using  a  thin  filler  with  a  smaller  crimp.  Do  not 
call  for  fillers  or  s])lice  plates  to  have  a  tight  fit,  as  this  is  impracticable  in 
the  shop.     The  stiffeners,  of  course,  should  have  a  close  bearing. 

Do  not  call  for  planing  ot  the  base,  cap,  sole,  or  masonry  plates,  as  the 
mills  can  roll  the  same  closer  than  they  can  be  planed. 


ECONOMICS    IN    DESIGN    FOR    SHOP    CONSIDERATIONS  207 

The  old  rule  of  sixty  degrees  for  single  lacing  should  be  abolished, 
because  this  makes  the  lacing  entirely  too  close  for  narrow  members,  and 
it  is  quite  expensive  and  unsightly.  Lacing  bars  should  generally  be  lapped, 
as  this  detail  will  save  about  half  the  rivets.  Instead  of  lacing  it  is  often 
advisable  to  employ  a  solid  web.  This  will  sometimes  permit  the  use  of 
lighter  main  angles  by  counting  the  web  as  part  of  the  section,  although  it 
reduces  the  radius  of  gyration  and  consequently  increases  the  sectional 
area  of  a  compression  member  —  besides,  it  greatly  facilitates  the 
painting. 

All  hand  riveting  should  be  avoided  wherever  possible,  also  all  odd 
riveting  that  has  to  be  done  either  before  the  work  is  assembled  or  after  a 
piece  is  otherwise  finished. 

In  short  plate-girder-spans  it  is  economic  to  omit  the  bottom  lateral 
system.  Lug  angles  on  laterals  are  expensive — it  is  better  to  use  larger 
connecting  plates  in  order  to  get  the  requisite  number  of  connecting  rivets. 

In  laying  out  viaducts,  as  many  towers  as  possible  should  be  made 
alike  by  varying  the  heights  of  the  pedestals. 

In  square-girder  spans,  the  number  of  panels  of  bracing  should  be 
even,  but  in  skew-girder  spans  it  should  be  odd.  The  greatest  amount  of 
duplication  in  any  skew-span  will  be  obtained  if  the  floor  is  laid  out  so 
that  the  entire  span  can  be  revolved  around  a  central  point. 

In  pin-connected  work  the  sizes  of  the  pins  should  not  be  varied  more 
than  is  strictly  necessary,  two  or  three  sizes  being  generally  sufficient  for 
one  span.  It  is  not  altogether  a  waste  of  material  to  use  larger  pins  than 
necessary,  as  the  bearing  plates  can  be  reduced  in  thickness  and  often  in 
length. 

It  is  economic  of  shopwork  to  avoid  running  the  top  flanges  of  stringers 
over  the  tops  of  the  cross-girders. 

In  riveted  tension  members  it  is  well  to  use  tie  plates  instead  of  lacing. 
The  former  have  the  advantage  of  getting  better  shop  rivets. 

It  is  not  necessary  that  the  web-plate  of  a  plate  girder  should  be  in  con- 
tact with  the  sole  plate,  and  to  make  it  so  is  expensive. 

In  deep  girders  the  web  thickness  should  not  be  less  than  ywo  oi  the 
depth  thereof,  as  otherwise  buckling  is  liable  to  occur. 

Where  webs  are  spliced,  ample  clearance  should  be  allowed,  and  the 
depth  of  the  web  should  be  one-half  inch  less  than  the  distance  from  out 
to  out  of  flange  angles. 

Rounded  corners  in  plate  girders  are  expensive,  but  sometimes  they  are 
required  for  the  sake  of  appearance.  Cambering  of  plate-girders  is  useless 
and  quite  expensive. 

Information  should  be  furnished  to  the  fabricating  shop,  specifying  the 
end  of  the  structure  which  is  to  be  erected  first,  it  being  very  desirable  to 
fabricate  the  work  in  the  order  of  erection  and  also  to  note  the  direction 
of  long  plate-girders,  so  as  to  save  turning  them  during  shipment,  at  the 
shop,  or  in  the  field. 


208  ECONOMICS   OF   BRIDGEWORK  Chapter  XXIII 

On  chord  or  column  sections  extending  over  two  panels  with  the  same 
depth  of  section,  but  with  smaller  area  required,  the  increased  weight  of  the 
shop  spHces  will  tend  to  offset  the  increase  in  weight  due  to  making  both 
sections  the  same,  the  big  advantage  in  the  latter  construction,  of  course, 
being  that  the  material  is  continuous  without  the  splice. 

Frequently,  on  stringers  and  hght  girders,  the  webs  are  designed  very 
light,  which  necessitates  the  use  of  many  stiff eners  to  prevent  buckhng. 
It  is  often  a  big  advantage  to  thicken  the  web  and  omit  the  stiff  eners.  The 
weight  in  either  case  is  about  the  same,  as  the  omission  of  the  stiffeners 
will  partially  offset  the  increased  weight  of  the  thicker  web. 

For  chord  sections,  the  employment  of  reinforcing  plates  between 
angles  should  be  avoided  by  using  additional  web-plates  the  full  depth  of 
the  chord.  This  design  has  the  advantage  of  connecting  more  of  the 
main  material  to  the  flange  angles  direct,  and  avoids  the  use  of  a  great 
many  rivets  which  are  necessary  to  connect  the  reinforcing  plates  to  webs. 
When  two  webs  are  riveted  together,  the  rivets  should  be  about  12"  from 
center  to  center,  the  edges  of  the  webs,  of  course,  being  held  together  by 
the  rivets  through  the  flange  angles. 

When  the  specifications  call  for  material  drilled  from  the  soHd  on  account 
of  the  use  of  either  alloy  steel  or  very  thick  ordinary  steel,  the  members 
should  be  designed  with  as  few  pieces  as  possible.  Instead  of  using  f " 
or  I"  plates,  which  generally  are  of  the  right  thickness  for. punched  work, 
the  material  should  be  ordered  as  thick  as  permissible  within  the  mill 
requirements,  provided  that  the  strength  of  the  plates  does  not  drop  below 
the  specification  stipulations  on  account  of  insufficient  rolhng. 


The  preceding  portion  of  this  chapter  applies  specially  to  the  practice 
of  the  consulting  engineer,  although  it  records  the  opinions  of  experts  in  the 
line  of  steel  manufacture;  but  the  following  pertains  specially  to  the 
drafting  work  in  the  office  of  a  bridge  manufacturing  company.  Its 
inclusion  is  in  the  nature  of  an  afterthought;  and  the  explanation  thereof 
is  as  follows: 

Long  after  the  supposed  finishing  of  the  chapter,  the  author  was  being 
shown  through  the  shops  of  the  American  Bridge  Company  at  Ambridge 
by  an  old  friend  of  his,  Mr.  C.  M.  Canady,  one  of  the  principal  engineers 
of  that  Company;  and  needing  additional  data  for  the  chapter  on  "Eco- 
nomics of  Shop  work"  he  persuaded  that  gentleman  to  promise  to  furnish 
some.  Wlien  the  notes  came  to  hand,  it  appeared  that  Mr.  Canady  had 
confined  his  remarks  entirely  to  the  economics  of  design  as  practiced  in  the 
Company's  drafting  office.  As  the  said  notes  are  of  great  value,  and  as 
they  supplement  and,  in  many  ways,  endorse  the  statements  herein  which 
precede,  the  author  decided  at  once  to  include  them  in  this  place;  and  they 
are,  consequently,  given  practically  verbatim. 


ECONOMICS    IN    DESIGN    FOR    SHOP    CONSIDERATIONS  209 

Principles  of  Economics  in  Bridge  Design  for  Shop  Considerations 

''  In  the  following  notes  relative  to  the  Economics  in  the  Design  of 
Bridges  for  Shop  Considerations,  the  Drawing  Room  attached  to  the 
Fabricating  Shop  has  been  considered  as  a  component  and  closely  related 
part  of  the  said  shop ;  and  points  that  facilitate  the  execution  of  shop  draw- 
ings have  been  included. 

"In  the  preparations  of  a  bridge  design  for  a  given  location,  making 
spans  duplicate  instead  of  different  lengths  has  not,  in  the  writer's  opinion, 
been  given  quite  the  attention  it  deserves.  Such  duplication  always  means 
decreased  cost  of  drawings  and  shop  work,  and  may  mean  also  the  adop- 
tion of  a  special  fabrication  programme  for  that  contract,  which  would 
further  reduce  costs. 

"  For  the  same  reason  the  design  should  lend  itself  to  the  maximum 
amount  of  duplication  in  the  details.  To  this  end  small  differences  in  the 
cross-section  of  main  members  should  be  shunned.  The  avoidance  of 
light  and  heavy  trusses,  on  account  of  a  sidewalk  on  one  side  only,  is  a  case 
in  point.  This,  however,  is  more  applicable  to  hght  work  and  to  where  the 
sidewalk  load  is  comparatively  small.  Otherwise,  where  there  is  a  mate- 
rial saving  in  weight  by  using  Kght  and  heavy  trusses,  the  difference  can 
generally  be  accomplished  by  increasing  the  thickness  of  component  parts 
of  the  various  sections  without  changing  the  dimensions  of  the  sections 
themselves,  thus  preserving  the  duplication  of  spacing  and  the  details  for 
the  two  trusses,  as  well  as  those  for  the  lateral-system  connections. 

"  Under  modern  mill  and  shop  conditions  it  is  economical  to  build 
bridges  with  longer  panels  than  formerly  used.  Longer  panels  mean  fewer 
joints  and  fewer  separate  pa.rts,  with  consequent  decrease  in  shop  and 
drawing-room  costs. 

''  If  members  can  be  made  symmetrical  about  a  point  midway  between 
the  ends,  it  counts  for  economy  in  the  preparation  of  drawings  and  templets. 

"  Often  spans  have  been  designed  with  a  small  skew  where  a  nominal 
increase  in  length,  due  to  making  the  span  square,  vv^ould  have  meant  a 
decided  saving  in  the  cost  of  the  structure  as  a  whole. 

''  In  the  design  of  a  deck-girder  bridge,  if  the  span  is  square,  it  is  econom- 
ical to  arrange  the  lateral  system  with  an  even  number  of  panels,  so  that 
the  girder  can  be  made  symmetrical  about  the  center. 

"  If  the  span  is  skewed,  use  an  odd  Aumber  of  panels,  so  that  the  girders 
can  be  made  alike  and  their  position  in  the  span  reversed.  Stringers  with- 
out cover  plates  should  have  an  odd  number  of  panels  of  laterals.  They  will 
then  have  the  same  punching  in  the  top  flanges  and  be  made  alike  for 
turning  end  for  end,  instead  of  different,  as  they  would  be  if  an  even  number 
of  panels  were  used. 

"  Some  Consulting  Engineers  and  occasionally  even  the  designing  offlces 
of  the  Bridge  Companies  are  prone  to  make  their  designs  so  complete  as 
to  be  almost  shop  drawings.     This  does  not  make  for  economy,  either  in 


210  ECONOMICS   OF  BRIDGEWORK:  Chapter  XXIII 

the  preparation  of  the  design  or  in  the  work  of  the  drawing  room.  Even 
where  considerable  freedom  is  allowed  in  the  way  of  modifications  to  suit 
the  standard  methods,  details,  and  equipment  of  the  particular  shop  doing 
the  work,  the  fact  that  such  modifications  must  be  arranged  for  with  the 
Engineer,  as  well  as  their  actual  accomphshment,  involves  a  certain  delay 
and  slowing  down  in  getting  the  work  under  way  in  the  drawing  room. 
The  engineers  thereof  must  necessarily  make  complete  investigation  of 
the  geometry,  fits,  etc.,  including  the  requisite  number  of  large-scale  lay- 
outs, independent  of  the  completeness  of  the  design.  The  manufacturer  is 
always  (and  properly  so)  held  responsible  for  the  coiTCct  fit  of  the  steelwork. 
The  Engineer's  preference  for  certain  types  of  details,  or  details  that  are 
required  by  the  conditions  of  erection,  should,  of  course,  be  indicated  as  a 
part  of  the  design. 

"  The  spacing  and  arrangement  of  rivets  should  not  be  fixed;  for  the 
limitations  of  the  specifications  as  to  the  maximum  and  minimum  spacing 
ought  to  be  sufficient.  The  designer  should  always  keep  in  mind  that 
modern  bridge  shops  are  equipped  with  multiple  punches  and  various 
spacing  devices,  and  that  contract  prices  are  based  upon  the  largest  possible 
use  of  such  machines.  Erection  difficulties  and  impossibihties  are  often 
incorporated  in  such  complete  designs,  which  objectionable  features  must 
be  'ironed  out'  by  the  engineer  responsible  for  the  shop  drawings  before 
the  detailing  can  go  ahead.  He  has  as  his  particular  field  the  following 
duties : 

"1.  To  make  details  for  carrying  out  the  specifications  and  properly 
developing  the  strength  of  the  parts  connected. 

"2.  To  detail  so  that  the  shop  can  fabricate  most  economically. 

"3.  To  detail  so  that  the  erection  methods  and  the  equipment 
determined  upon  for  the  particular  bridge  shall  be  not  only 
possible  but  economical  as  well.  The  sequence  in  the  placing 
of  the  different  members  must  be  taken  account  of  throughout 
the  entire  detaihng. 

"  The  engineer  at  the  plant,  versed  in  the  preparation  of  shop  drawings, 
is  both  by  experience  and  environment  the  best  qualified  man  to  meet 
these  three  necessities.  In  fact,  the  last  two  are  never  possible  of  final 
solution  until  after  the  contract  has  been  signed  and  the  work  is  being 
developed  in  the  shop  drawing  room. 

"  It  is,  of  course,  conceded  that,  for  unusual  or  monumental  structures, 
the  makeup  of  the  details  is  so  interwoven  with  the  general  design  that 
the  development  of  the  two  must  proceed  together.  Even  in  such  cases 
it  is  nearly  always  necessary  for  the  best  results  that  modifications  be  made 
as  the  work  progresses  in  the  drawing  room. 

"  The  corre(^tness  of  the  foregoing  statements  has  been  proved  by  the 
actual  experience  of  our  Shop  Engineers  covering  their  work  reaching  over  a 
period  of  the  past  twenty  years.     We  are  now  so  wcH  fortified  with  examples 


ECONOMICS    IN    DESIGN    FOR    SHOP    CONSIDERATIONS  211 

of  the  boet  practice  for  different  types  of  bridges  that  there  is  no  great 
difficulty  in  reahzing  the  true  intent  of  the  design  in  the  study  of  the 
structure  that  must  be  made  in  the  shop  drawing  room.  It  would  seem  to 
be  wise  economy  on  the  part  of  the  designing  engineer  to  take  full  advantage 
of  these  facts. 

''  For  full-punched  work,*  with  splices  in  chords  reamed  to  fit,  it  is  im- 
portant that  the  design  should  provide  for  the  next  larger  sized  rivet  in  the 
reamed  splices.  This  saves  in  the  shop  one  handling  of  all  the  main  parts, 
because  one  size  of  punched  holes  wiU  answer  for  both  reamed  and  unreamed 
holes.  If,  for  instance,  |"  rivets  are  being  generally  used,  and  allowance 
is  not  made  in  the  des'gn  for  larger  punching  than  yf",  it  is  necessary  to 
punch  xf"  holes  in  the  body  of  the  member  and  rehandle  all  the  long  main 
parts  in  order  to  punch  a  smaller -sized  hole  (say  yf "  diameter)  at  the  ends 
where  the  splice  is  to  be  reamed  for  fit.  If  allowance  is  made  in  the  design 
for  Ire"  holes,  the  punching  throughout  will  be  jf "  and  the  splices  will 
then  be  reamed  out  to  1]^",  thus  saving  the  extra  handling  at  the  punch. 

"  In  heavy,  reamed  girder- work  where  several  cover  plates,  side  plates, 
and  heavy  flange-angles  are  used,  the  size  of  the  sub-punched  holes  should 
be  not  less  than  jf "  diameter.  It  is  difficult  and  expensive  to  fit  up  such 
work  where,  because  of  the  size  of  sub-punched  holes,  smaller  fitting-up 
bolts  are  necessary.  This  is  because  of  the  great  difficulty  in  properly 
pulling  together  such  heavy  parts  and  so  many  of  them  with  f "  fitting-up 
bolts.  For  work  not  properly  brought  together  in  fitting,  the  riveting  is 
expensive  and  apt  to  be  imperfect. 

"  It  almost  goes  without  saying  that  Forge  and  Machine  Shop  work 
should  be  kept  at  a  minimum.  Bending  of  long  pieces  is  particularly 
undesirable,  because,  when  a  long  angle,  for  instance,  is  to  be  bent,  the 
operation  of  heating  and  bending  disorganizes  and  interferes  with  all 
the  adjacent  operations  in  the  shop.  Making  a  bend  at  each  end  of 
a  long  angle,  channel,  or  beam  is  not  only  quite  expensive,  but  next  to 
impossible  to  do,  because  of  the  extreme  difficulty  in  maintaining  the 
correct  measurement  between  bends. 

"  Curving  ends  of  girders  is  a  considerable  item  of  extra  shop  expense. 
It  adds  to  the  cost  of  drawings,  templets,  laying  out,  punching,  assem- 
bling, and  riveting,  in  addition  to  the  extra  cost  of  bending  the  end  angles. 
In  fact,  it  is  doubtful  if  the  aesthetic  value  is  enhanced  at  all  in  proportion 
to  the  increased  price  which  the  buyer  must  pay.  However,  where  it  is 
decided  to  use  'round  ends,'  the  exact  radius  of  the  curve  should  be  left 
to  the  shop  detailer,  so  that  standard  bending  forms  may  be  used. 

'■  Staggered  riveting  invites  shop  errors  and  slows  down  the  work.  Pref- 
erence should  be  given  to  rivets  placed  opposite  or  in  single  rows,  where 
the  necessities  of  design  do  not  require  that  they  be  staggered.  The 
different  members  of  a  span  should  be  designed,  as  far  as  possible,  to  allow 


The  author  is  opposed,  on  general  principles,  to  punching  any  rivet  holes  full  size. 


212  ECONOMICS   OF   BRIDGEWORK  Chapter  XXIII 

the  use  of  power  riveters.  This  is  especially  applicable  to  box  sections  with 
the  flanges  of  channels  turned  in.  In  general,  the  clear  distance  in  such 
cases  should  be  not  less  than  5^"  or  6". 

"  Avoid  sections  calh.ng  for  the  use  of  a  variety  of  sizes  of  shop  and  field 
rivets  in  the  same  span  or  structure. 

''For  narrow,  '  I '-shaped  sections,  preference  should  be  given  to  four 
angles  with  a  web  plate  instead  of  four  angles  laced.  Often  for  such  narrow 
sections  the  latticed  type  accomplishes  very  httle  or  no  saving  in  weight, 
and  the  shop  expense  is  greater  and  the  result  is  less  desirable  from  a 
maintenance  standpoint,  as  compared  with  the  plate-and-four-angle 
section. 

"  Quite  often  a  small  increase  in  the  thickness  of  stringer  webs  will 
eliminate  the  necessity  for  the  use  of  stiff eners. 

"  Designers  very  often  do  not  make  enough  allowance  between  gross  and 
net  section  for  the  proper  maintenance  of  the  latter  and  at  the  same  time 
for  the  preservation  of  rational  details  at  the  critical  points.  For 
instance,  according  to  the  1920  specifications  of  the  American  Railway 
Engineering  Association,  if  only  one  |"  rivet  hole  is  allowed  out  of  an 
angle,  the  stagger  must  be  four  inches;  and  other  specifications  have  been 
more  stringent.  If  the  piece  happens  to  be  a  Q"X4:"  angle  with  two  rows 
of  rivets  in  the  six-inch  leg,  the  detailer  is  in  trouble  at  once  with  the  loca- 
tion of  rivets  in  the  four-inch  leg  adjacent  to  the  critical  section.  He  is 
often  compelled  to  give  it  up  and  encroach  on  net  section  after  he  has 
wasted  a  lot  of  valuable  time  in  trying  to  meet  the  conditions.  Any  angle 
with  punching  in  both  legs,  used  in  tension,  should  have  two  rivet  holes 
deducted  from  the  gross  section. 

"In  plate-girder  work,  fillers  under  stiff ener  angles  should  not  be  required 
to  fit  tight  against  flanges.  The  overrun  in  width  of  flange  angles,  often 
varying  for  the  different  angles  on  a  single  girder,  means  the  re-cutting  and 
fitting  of  fillers  to  suit.  This  results  in  a  slowing  down  and  an  increased 
cost  in  the  work  of  fitting  uj)  the  girder  for  riveting.  A  clearance  of  at 
least  I"  should  be  permitted  at  each  end  of  filler. 

"  All  unnecessary  bevel  cuts  on  the  ends  of  long  angles,  plates,  or  other 
shapes  should  be  dispensed  with.  These  are  mu(;h  more  cxi:)ensive  to 
make  on  long  i)icceK  than  on  small  detail  parts.  It  seems  somewhat  absurd 
carefully  to  cut  the  end  of  an  angle  to  bevel,  for  the  sake  of  apjieaiance, 
when  it  is  not  exposed  to  view  in  the  finished  structure.  IndeiHl,  the 
sesthetic  value  of  such  bevel  cuts  is  very  much  in  ({uestion,  excejit  where  a 
projecting  corner  is  exposed  to  the  skyline. 

"  The  ends  of  columns  for  viaducts  or  other  structures  resting  on 
masonry  can  often  ])e  made  less  expensive  in  hoih  wcnght  and  workman- 
ship by  using  thicker  base  plates  and  omitting  vertical  stiffening  angles 
with  their  extrmsive  arrangement  of  wing-i^lates  that  are  intended  to  help 
in  the  distribtition  of  the  load. 

"  Finally,  and  in  general,  the  designer  should  give  the  most  careful  atten- 


ECONOMICS    IN    DESIGN    FOR    SHOP    CONSIDERATIONS  213 

tion  to  tho  coordination  of  the  different  parts  of  his  design,  so  that  it  can 
be  detailed  in  the  simplest  and  most  natural  manner  with  the  elimination, 
as  far  as  possible,  of  cumbersome  or  complicated  joints  and  connections. 
In  determining  the  makeup  of  the  different  sections,  the  detailing  possibili- 
ties should  be  given  much  weight,  for  quite  frequently  they  are  the  deter- 
mining factor." 


CHAPTER  XXIV 


ECONOMICS   IN   DESIGN    FOR   ERECTION    CONSIDERATIONS 


The  tyro  in  bridge  designing,  no  matter  how  profound  may  be  his 
theoretical  knowledge,  often  falls  down  very  hard  untU  he  has  learned 
through  sad  experience  that  the  erectors  of  structural  steelwork  have  cer- 
tain standard  requirements  which  must  be  observed.  If  they  be  ignored, 
the  work  is  often  seriously  delayed;  and,  as  delays  in  the  field  are  exceed- 
ingly expensive,  the  matter  of  making  the  designs  so  that  aU  the  metal 
wiU  go  together  easily  and  expeditiously  involves  engineering  economics  of 
great  importance. 

The  failure  to  furnish  sufficient  clearance  is  generally  the  tj^ro's  first 
offense — and  it  certainly  is  a  serious  one.  If  the  designer  who  commits 
this  blunder  could  hear  what  the  bridge  erectors  say  about  him,  his  ears 
would  certainly  tingle. 

Mr.  Wolfel's  general  instructions  concerning  designing  to  meet  field 
requirements  are  as  follows: 

(1)  Allow  ample  clearance  for  aU  entering  connections. 

(2)  Provide  erection  shelves  for  girders  and  beams,  particularly  when  they  frame 
opposite  each  other. 

(3)  Have  all  riveting  arranged  in  such  a  way  that  it  can  follow  the  erection  of  the 
work.  Riveting  should  never  be  allowed  to  interfere  with  the  raising  and  placing  of 
the  steel. 

(4)  Be  sure  that  cross  frames  in  deck  bridges  can  be  swung  in  place  without  spread- 
ing the  girders. 

(5)  Be  careful  in  through  plate-girders  to  arrange  the  stiffeners  so  that  the  floor- 
beams  and  stringers  can  be  put  in  place  with  the  girders  in  their  final  position. 

(6)  Arrange  the  riveting  around  the  ends  of   the  spans  so  that  the  rivets  can  be 

driven  with  the  steel  in  the  final  posi- 
tion. It  should  never  be  necessary  to 
jack  up  spans  to  drive  rivets. 

(7)  In  trough  floorwork,  especially 
where  the  under  clearance  is  small, 
arrange  the  design  so  that  all  field  rivets 
can  be  driven  from  the  top,  as  in  Fig.  24a. 

(8)  While  it  has  been  customary  to 
call  for  25  per  cent  excess  for  all  field 
rivets,    10   per   cent   excess   should  be 


Fig.    24o. 


Trough-Floor    Construction   for 
Easy  Field  Riveting. 


sufficient,  if  the  rivets  are  driven  with  air  hammers. 

On  this  subject  Mr,  Reichmann  has  written  thus: 

The  designer  should  always  remember  to  allow  plenty  of  clearance  at  the  ends  of 
sheared  members  so  as  to  take  up  variations  of  shopwork.  One-half  inc^h  clearance  is 
considered  a  minimum  for  sheared  ends.     l'\)r  enteruig  connections,  plenty  of  clearance 

214 


ECONOMICS    IN    DESIGN    FOR    ERECTION    CONSIDERATIONS      215 

should  be  allowed,  as  a  great  many  of  the  difficulties  in  erection  are  due  to  lack  of 
clearance;  besides,  giving  reasonable  clearance  will  permit  of  more  rapid  shopwork  and 
the  avoidance  of  many  errors  in  the  field  due  to  inaccuracies  thereof. 

It  is  often  advisable  to  provide,  in  addition  to  the  usual  allowance  for  expansion,  a 
small  amount  for  erecting  the  metal,  due  to  what  is  called  the  "growth  of  steel."  For 
viaducts  such  adjustment  should  be  provided  about  every  400  feet;  and  similarly  for 
mill-building  work  it  is  necessary  to  consider  effects  of  adjustment,  even  if  it  is  decided 
not  to  take  care  of  expansion,  while  in  other  structures  the  joints  for  expansion  wUl  also 
serve  the  purpose  of  adjustment. 

The  expansion  points  for  stringers  or  elevated  raUroad-girders,  where  pockets  are 
used,  sometimes  have  not  enough  space  behind  the  end  stiffeners  of  the  expansion 
girders  to  allow  for  the  insertion  of  rivets  through  the  end  connections  of  the  fixed 
girders.  It  should  be  remembered  that  the  expansion  stringers  and  the  fixed-end 
stringers  are  erected  before  the  rivets  in  the  connection  of  the  fixed  stringers  are  driven. 

When  columns  are  set  to  stone  bolts,  which  have  been  imbedded  in  masonry,  the 
holes  should  be  |"  or  1"  larger  than  the  diameter  of  the  bolt,  so  as  to  provide  adjustment 
to  take  care  of  the  inaccuracies  in  setting  the  bolts  in  the  concrete. 

A  common  mistake  in  design  is  to  proportion  the  members  with  too  small  a  width, 
causing  considerable  trouble  in  packing  the  pins  and  in  making  room  for  the  verticals, 
pin  plates,  etc.  Another  bad  feature  of  narrow  chords  is  that  practically  all  rivets 
around  the  connections  must  be  countersunk  because  of  close  space,  and  the  ends 
of  the  posts  must  be  cut  away  for  clearance,  thereby  weakening  the  said  ends.  By 
adopting  chords  of  larger  widths  much  better  details  can  be  used  around  the  pins  at 
panel-points. 

When  two  or  more  truss  spans  are  identical,  or  when  they  are  similar  and  have 
the  same  field  connections,  the  field  holes  should  be  reamed  to  an  iron  templet,  in  place  of 
reaming  them  while  the  members  are  assembled.  This  will  facilitate  the  delivery  of  the 
work,  and  wUl  make  identical  members  throughout  the  structure  interchangeable. 
The  advantages  in  the  field  are  evident,  less  time  being  spent  in  sorting  and  finding 
material. 

In  the  designing  of  details  extreme  care  shoiild  be  exercised  in  arranging  all  joints 
and  connections,  so  that  the  work  cannot  only  be  buUt  at  the  shop  for  the  least  cost 
in  labor  and  material,  but  also  that  it  may  be  erected  most  economically  and  with  a 
minimum  of  risk.  In  the  case  of  bridgework,  all  connections  should  be  so  detailed 
that  spans  can  be  connected  and  made  self-sustaining  and  safe  in  the  shortest  possible 
time. 

Unless  for  special  reasons,  it  is  usually  customary  to  begin  the  erection  of  pin- 
connected  spans  at  the  center  panel,  as  this  panel  has  adjustable  members  and  the 
trusses  can  be  squared  up  there  before  proceeding.  The  details  should,  therefore,  be 
so  arranged  that  the  center  panel  can  be  completed  and  made  self-sustaining  before  the 
traveler  is  moved  to  the  next  panel.  It  is  the  usual  custom  for  the  erection  to  pro- 
ceed from  the  center  panel  toward  the  fixed  end,  and  after  this  half  of  the  span  is  erected, 
to  proceed  toward  the  roller  end.  Top  chord  sections  in  any  particular  panel  are  put 
in  place  after  the  posts  and  bars  are  erected;  and  it  is  especially  desirable  in  heavy 
work  that  the  details  be  so  arranged  that  these  chord  sections  can  be  lifted  above  the 
posts  and  set  directly  in  place  without  being  moved  on  end  or  sideways.  Therefore, 
plates  connecting  two  adjoining  chord  sections  in  heavy  work  should  always  be  shipped 
loose. 

Wherever  possible,  in  all  truss  spans  the  floor  connections  should  be  so  arranged 
that  the  floor  system  can  be  put  in  place  either  before  or  after  the  trusses  have  been 
erected  in  their  final  position.  It  is  usually  customary,  where  local  conditions  will 
permit,  to  put  the  floor  system  in  place  first  and  erect  the  trusses  afterward.  This 
method  of  procedure  has  a  great  many  advantages  over  that  of  raising  the  trusses  first, 
viz.:   there  is  a  large  saving  in  falsework,  as  longer  panels  can  be  used,  putting  bents 


216  ECONOMICS   OF   BRIDGEWORK  Chapter  XXIV 

directly  under  the  panel-points  and  using  the  new  floor  system  for  carrying  traffic  and 
for  running  out  material  for  the  trusses;  it  permits  the  posts  to  be  bolted  to  the  floor- 
beams  and  released  from  the  tackles  on  the  travelers;  it  fixes  the  exact  position  of  the 
shoes  on  the  piers  so  that  we  can  proceed  with  the  erection  from  the  center  either  toward 
the  fixed  or  the  roller  end,  as  we  may  prefer;  it  has  the  advantage  of  giving  more 
opportunity  for  jacking  up  the  spans  in  order  to  secure  proper  camber;  and  it  requiers 
a  minimum  amount  of  blocking.  There  are  other  featm-es  which  render  it  desirable, 
where  possible,  to  erect  the  floor  system  in  advance  of  the  trusses.  Over  dangerous 
streams,  however,  where  there  is  a  possibility  of  loss  during  the  erection,  it  is  some- 
times desirable  to  erect  the  trusses  first,  so  as  to  have  as  little  material  on  the  false- 
work as  practicable  and  thus  minimize  the  amount  endangered.  There  are  also  some- 
times certain  local  conditions  which  make  it  imperative  that  the  trusses  be  erected 
first;  and,  therefore,  it  is  important,  wherever  possible,  that  details  be  so  arranged 
that  either  method  can  be  used.  In  the  erection  of  through,  riveted,  lattice  spans,  it 
is  customary  to  place  the  floor  system  first,  then  to  put  the  lower  chords  in  position, 
set  up  the  web  members,  and  put  the  top  chords  on  last.  Therefore,  it  is  more  advan- 
tageous to  have  the  gusset-plates  connecting  the  web  members  with  top  chord  riveted 
to  the  top  chord  sections  rather  than  to  posts  or  diagonals,  as  the  rivets  in  gusset- 
plates  connecting  top  chords  with  web  members  are  more  easily  driven  in  the  web 
members  than  in  the  top  chord  sections. 

In  the  case  of  through  plate-girders,  the  details  of  the  floor  system  should  be 
so  arranged  that  the  stringers  and  floor-beams  can  be  put  in  place,  panel  by  panel, 
without  the  necessity  of  spreading  the  main  girders.  Particularly  is  this  the  case  in 
"Rolling  Lift  Bridges,"  which,  in  the  majority  of  cases,  have  to  be  erected  in  an  upright 
position,  and  where  it  is  extremely  dangerous  and  practically  an  impossible  operation 
to  spread  the  trusses  in  order  to  put  in  place  the  floor  system. 

Top  chord  sections  with  half  pin-holes,  having  a  hinge-plate  on  each  section,  are 
undesirable.  When  half  pin-holes  are -used,  if  possible  put  a  hinge-plate  on  one  sec- 
tion only  and  make  it  long  enough  to  rivet  or  bolt  to  the  adjoining  section  when  in 
place.  Hinge-plates  should  be  arranged  so  as  to  give  two  full  pin-holes  in  center  chord 
sections,  and  should  be  put  on  the  ends  farthest  from  the  center  on  the  other  sections, 
except  in  special  cases  when  it  is  necessary  to  commence  raising  spans  from  the  end 
instead  of  the  center. 

Entering  connections  are  usually  the  most  difficult  and  expensive  to  make;  and 
v/here  at  all  possible,  entering  connections  of  any  character  should  be  avoided,  but 
where  they  must  be  used,  particular  attention  should  be  given  to  insure  necessary 
clearances.  An  entering  connection  is  not  only  an  expensive  and  dangerous  operation, 
but  in  a  great  many  cases  it  cannot  be  accomplished  on  account  of  the  interference 
with  back  walls,  adjoining  spans,  etc. 

It  is  of  the  ^-^reatest  importance  to  allow  ample  clearance  where  members  are 
packed  inside  of  chords,  posts,  etc.,  as  lack  of  proper  clearance  causes  much  trouble 
and  expense,  not  only  augmenting  the  cost  of  erection  by  increasing  the  time  required 
for  making  the  span  safe,  but  adding  materially  to  the  risk.  In  putting  in  tie-bars 
and  diagonals,  it  is  customary  to  connect  them  on  the  bottom  chord  pins  first,  and  then 
swing  them  into  the  chords  and  posts  around  the  lower  pins  as  a  center.  All  rivet 
heads  coming  in  the  path  of  bars  swung  in  this  way  should  be  cleared.  Too  much 
attention  cannot  be  given  to  this  matter  of  proper  clearance.  Particularly  is  this  the 
case  in  through  and  deck  riveted  lattice  spans,  which  are  being  erected  now  more  than 
ever  Ix^fore  with  the  use  of  a  derrick  car  with  one  boom;  and  the  ai)pliances  for  pull- 
ing tight-fitting  members  into  place  are  not  always  present,  as  was  the  case  formerly 
when  these  spans  were  erected  by  a  gantry  traveler.  For  adjustable  rods  packed  close 
together,  the  sleeve  nuts  should  be  staggered.  Attention  .should  be  given  to  the  field 
connections  so  that  enough  space  is  allowed  around  all  field  rivets  to  enable  them  to 
be  driven, 


ECONOMICS    IN    DESIGN    FOR    ERECTION    CONSIDERATIONS      217 

All  lateral  bracing,  hitch  plates,  rivet  heads  in  laterals,  etc.,  should  be  kept  enough 
below  the  level  of  the  top  chords  of  girders,  stringers,  etc.,  so  that  the  ties  when  in 
place  will  not  foul  them,  it  being  an  expensive  operation  to  notch  ties  to  clear  such 
obstructions. 

Where  laterals  and  hitch  plates  do  not  interfere  with  the  loading  of  girders,  and 
are  not  of  such  character  as  wiU  allow  them  to  be  easUy  broken  off,  they  should  be 
riveted  to  the  said  girders;  otherwise  they  should  be  shipped  loose  or  riveted  to  the 
braces. 

Particular  attention  should  be  given  to  the  question  of  field  riveting.  Details 
should  be  closely  examined  with  a  view  of  minimizing  the  number  of  field  rivets. 

It  is  not  advisable  to  put  two  shoes  on  one  bed-plate;  but  if  this  cannot  be  avoided, 
the  bed-plate  should  be  made  longer  and  the  anchor  holes  should  be  slotted  to  allow  for 
variations  in  masonry. 

The  following  are  the  most  important  points  to  be  observed  in  detaUing,  Ib  order  to 
facilitate  and  cheapen  erection. 

(a)  Avoid  as  far  as  possible  entering  connections. 

(b)  See  that  proper  clearances  are  given. 

(c)  Minimize  the  number  of  field  rivets. 

Viaducts 

When  the  track  is  on  a  grade  and  the  grade  is  not  very  steep,  make  the  two  bents 
of  one  tower  alike  by  adding  filler  plates  on  the  tops  of  the  up-grade  columns.  For 
steep  grades  make  the  two  bents  of  one  tower  the  same  length,  but  square  the  longi- 
tudinal bracing.  A  good  detailer  will  then  make  the  punching  the  same  on  all  four 
columns  of  the  tower,  but  the  gusset  plates  which  connect  to  the  longitudinal  bracing 
will  be  different  for  the  two  bents. 

When  designing  colunms  for  the  towers,  the  splices  should  be  indicated  so  that 
the  column  sections  should,  preferably,  be  imder  40'  long,  but  should  not  under  any  cir- 
cumstances exceed  60'. 

Where  two  deck  girder  spans  are  adjacent,  the  end  cross-frames  are  placed  close 
to  the  ends  of  the  girders.  The  cross-frames  cannot  be  set  by  swinging  in  from  the 
end  of  the  span.  They  must  be  erected  by  swinging  in  from  the  center  of  the  span. 
The  stiffener  angles  carrying  the  cross  girders  should  be  built  with  the  back  of  the 
angles  toward  the  center  of  the  span. 


CHAPTER  XXV 

ECONOMICS   OF   REINFORCED-CONCEETE    BRIDGES 

Reinforced-concrete  structures  being  the  most  modern  of  all  the 
general  types  of  bridge  construction,  it  is  not  to  be  expected  that  the 
economics  of  their  designing  should  be  so  highly  developed  as  in  the  case 
of  any  of  the  older  types.  Nevertheless  much  has  been  learned  about  the 
subject  through  the  numerous  investigations  made  for  the  author's  firms 
by  a  number  of  young  computers  during  the  last  twelve  or  fifteen  years. 
Practically  all  that  was  known  concerning  it  in  1915  was  stated  in  Chapter 
LIII  of  "Bridge  Engineering";  and  an  elaboration  of  that  treatment 
will  be  given  herein,  supplemented  by  the  results  of  a  series  of  investiga- 
tions made  specially  for  this  book. 

The  first  topic  for  economic  discussion  is  that  of 

Reinforcing  Steel 

At  the  present  time  one  of  the  mooted  points  in  the  designing  specifica- 
tions for  reinforced-concrete  bridges  is  the  proper  intensity  of  working 
stress  for  the  reinforcing  bars.  It  is  generally  conceded  that  it  should  not 
exceed  one-half  of  the  elastic  limit  of  the  metal;  and,  in  consequence, 
engineering  practice  in  the  past  has  Umited  it  to  16,000  lbs.  per  square 
inch,  but  a  number  of  manufacturers  now  desire  to  raise  it  to  18,000  lbs.  per 
square  inch  by  using  a  higher-carbon  steel — notably  re-roUed  steel.  Of 
course,  the  higher  intensity  saves  in  \he  quantity  of  steel,  but  generally 
increases  the  amount  of  concrete  required ;  because  the  higher  stress  in  the 
steel  reduces  the  moment  of  resistance  of  the  concrete  about  six  per  cent. 
If  the  amount  of  concrete  is  increased,  the  net  saving  is  about  two  (2) 
per  cent  in  slabs  and  three  (3)  per  cent  in  beams;  but  if  the  section  of  the 
concrete  is  determined  by  shear  or  other  considerations,  so  that  no  increase 
is  necessary,  those  percentages  will  be  increased  by  unity. 

There  are  two  grave  objections  to  usmg  the  higher  steel,  \'iz. : 
First.     When  bent  cold  it  is  liable  to  crack  on  account  of  its  increased 
hardness,  and 

Second.     It  tends  to  open  up  cracks  m  the  concrete. 

For  these  reasons  the  author  is  not  willing  to  use  such  steel  in  his  prac- 
tice; and,  on  general  principles,  he  is  opposed  to  the  employment  of  any 
re-rolled  metal,  because  of  the  temptation  for  the  mnnufactm-er  thereof  to 
run  in  all  kinds  of  old  materials — even  wornout  Bessemer  rails. 

218 


ECONOMICS   OF   REINFORCED-CONCRETE   BRIDGES  219 

Intensity  of  Working  Stress  for  Concrete 

For  many  years  the  author's  practice  has  been  to  stress  the  concrete  in 
compression  only  six  hundred  (600)  pounds  per  square  inch;  but  lately 
the  Joint  Committee  of  the  Technical  Societies  has  reported  in  favor  of 
adopting  six  hundred  and  fifty  (650)  pounds.  When  a  good  aggregate  is 
procurable,  the  author  has  no  objection  to  this  increase  of  eight  per  cent; 
but  otherwise  he  prefers  to  adhere  to  his  old  custom,  especially  as  by  so 
doing  he  adds  only  two  per  cent  to  the  cost  of  the  concrete  in  those  cases 
where  the  section  can  be  reduced  by  using  the  higher  intensity.  Very 
often,  though,  no  such  reduction  is  practicable,  and  the  saving  on  the 
entire  job  reduces  to  only  one  per  cent. 

The  actual  reduction  in  the  amount  of  concrete  in  a  beam  due  to  this 
difference  of  intensity  of  working  stress  is  about  six  per  cent,  but  this  is 
partially  offset  by  an  increase  in  the  amount  of  steel  required.  The  com- 
bination of  the  intensities  of  600  for  concrete  and  16,000  for  steel  requires 
a  percentage  of  0.68  for  reinforcing  steel,  while  with  650  and  16,000  that 
figure  is  increased  to  0.77.  Moreover,  construction  work  is  simplified  by 
using  more  concrete  and  less  steel,  also  better  concrete  is  secured;  hence 
the  author  does  not  think  that  there  is  much  real  advantage  in  adopting 
the  higher  intensity.  The  general  complaint  from  contractors  on  his  work 
has  been  "too  much  steel";  and  adopting  the  higher  intensity  for  concrete 
would  make  matters  worse.  Moreover,  the  use  of  heavier  concrete  sections 
tends  to  keep  down  the  shear  intensity,  which  is  always'  desirable. 

Frequently  there  is  a  choice  between  a  heavy  concrete  section  with  no 
shear  reinforcement,  and  a  lighter  section  with  such  reinforcement.  In 
superstructure  it  is  generally  preferable  to  adopt  the  latter  and  in  sub- 
structure the  former. 

Pavings 

The  subject  of  the  economics  of  pavings  is  treated  fully  in  Chapter  XXI. 
The  economy  lies  in  the  cost  of  the  pavement  itself,  excepting  that  brick 
is  heavier  than  the  other  paving  materials;  and,  consequently, 'it  adds  to 
the  cost  of  a  concrete  structure,  the  amount  being  from  two  to  three  per 
cent. 

It  is  poor  economy  to  neglect  the  expansion  joints  in  block  pavements; 
because  expansion  is  sometimes  quite  destructive,  not  only  causing  waves 
in  the  pavement  but  sometimes  actually  pushing  off  the  curbs. 

Handrails 

Handrails  for  reinforced-concrete  bridges  should  always  be  made  of 
concrete,  in  order  to  harmonize  with  the  rest  of  the  structure.  A  steel 
railing  on  a  concrete  bridge  is  ruinous  to  the  general  appearance,  and, 
therefore,  should  not  be  tolerated.  The  first  costs  of  the  two  types  of 
railing  are  about  alike;  but  the  concrete  one,  being  heavier,  requires  more 


220  ECONOMICS   OF   BRIDGEWORK  Chapter  XXV 

material  for  its  support.  Artistic  rails  are  more  expensive  than  plain 
ones;  hence  the  selection  of  the  design  will  often  involve  a  compromise 
between  economics  and  sesthetics,  and  wlU  depend  greatlj-  upon  the 
amount  of  money  available  for  the  work. 

Rails  can  be  built  entirely  in  place,  or  they  may  be  either  partly  or 
wholly  cast  in  sections  and  set  in  position.  The  jointing  will  require  care- 
ful attention;  for,  otherwise,  the  railing  will  have  a  bad  appearance  and 
even  may  go  to  pieces.  A  better  character  of  construction  can  be  secured 
with  separately-moulded  work;  but  unsightly  joints  would  offset  this 
advantage.  Separately-moulded  rails  generally  interfere  much  less  than 
other  types  of  rails  with  the  progress  of  construction ;  besides,  the  moulding 
of  the  parts  can  be  carried  on  at  odd  times  in  the  intervals  of  other  work. 
Both  of  these  features  are  money  savers. 

Designs 

The  economics  of  design  are  rather  difficult  to  determine,  as  the  quanti- 
ties involved  are  influenced  quite  largely  by  the  individual  tastes  of  the 
designer.  The  problem  is  also  complicated  by  the  facts  that  the  unit  costs 
of  the  various  portions  of  a  structure  may  be  more  or  less  different,  and  that 
the  unit  costs  of  different  types  of  construction  may  be  decidedly  unHke. 
In  general,  it  may  be  said  that  the  unit  costs  are  lower  for  those  struc- 
tures which  have  the  smiplest  form-work;  and  a  reduction  will  also  be 
effected  by  decreasing  the  area  of  form-surface  per  cubic  yard  of  concrete. 
For  instance,  in  the  case  of  a  wall  or  slab,  the  fojm-cost  per  cubic  yard  will 
vary  practically  inversely  as  the  thickness  of  the  said  wall  or  slab.  Evi- 
dently, therefore,  it  is  desirable  to  concentrate  the  concrete  into  a  few  large 
members,  rather  than  to  employ  a  great  number  of  small  ones. 

It  should  be  noted  that  reinforcing  bars  less  than  f "  in  diameter  com- 
mand higher  pound  prices  than  do  the  larger  bars.  The  extras  for  these 
small  bars  may  be  found  in  Engineering  News-Record  in  the  first  issue  of 
each  month. 


The  economics  of  the  designing  of  the  different  parts  of  reinforced- 
concrete  structures  will  now  be  discussed  in  logical  order. 

Slabs 

A  primary  economic  problem  in  slab  designing  is  that  of  two-way  versus 
one-way  reinforcing.  Two-way  reinforcing  involves  less  concrete  but  more 
steel  than  does  one-way  reinforcing;  hence  it  has  but  little  advantage, 
unless  the  reduction  of  dead-load  to  a  minimum  be  of  prime  hnportance. 

Different  arrangements  of  slab  steel  are  discussed  on  pages  918  to  921, 
inclusive,  of  "Bridge  Engineering";  and  it  will  be  noted  therefrom  that 
there  is  very  little  difference  in  the  weights  of  the  various  types.     Lighter 


ECONOMICS   OF  REINPORCED-CONCRETE   BRIDGES  221 

arrangements  of  steel  are  generally  used  in  buildings;  but  roadway  slabs, 
in  view  of  the  heavy  concentrated-live-loads  that  they  have  to  carry,  and 
which  produce  large  shears  throughout  and  positive  moments  over  almost 
the  entire  span,  require  carefully  and  liberally  designed  reinforcement. 

Barring  most  of  those  in  railway  bridges,  slabs  are  usually  continuous 
over  panel  points,  excepting  at  the  expansion  joints.  There  is  but  little 
difference  in  the  actual  costs  of  continuous  and  non-continuous  slabs; 
but  continuity  is  desirable  from  the  standpoints  of  paving  and  drainage; 
also  with  continuous  slabs  T-beam  construction  can  be  employed — involv- 
ing the  saving  of  much  material  in  girders.  The  continuity  of  slabs  and 
girders  complicates  construction  problems — sometimes  very  seriously. 
The  various  processes  of  the  construction  of  a  proposed  design  should  be 
studied  through  completely  in  order  to  make  certain  that  no  impracticable 
or  unnecessarily  expensive  work  is  involved.  Frequently  important 
savings  can  thus  be  effected ;  and  sometimes  it  is  found  cheaper  in  the  long 
run  to  use  more  concrete  than  the  minimum  practicable  amount.  For 
instance,  a  sidev/alk  slab  usually  rests  upon  the  curb,  which  in  turn  rests  on 
the  roadway  slab;  and  in  the  designing  it  is  advisable  to  provide  for  a 
construction  joint  at  the  top  of  the  roadway  slab,  because  it  would  b3  both 
difficult  and  expensive  to  pour  the  curb  and  the  sidewalk  slab  simulta- 
neously with  the  roadway  slab.  Such  construction  joints  can  be  arranged 
for  by  the  designer  without  involving  much  extra  expense,  provided  that 
he  gives  the  matter  proper  consideration  at  the  outset. 

Girders 

Girders  are  of  two  main  types,  single  or  continuous;  and  there  is  no 
great  difference  in  their  costs,  there  being  more  concrete  but  less  steel  in  the 
simple-span  type.  The  two-span-continuous  type  is  nearly  always  a  little 
more  expensive  than  the  simple-span  type.  The  simple-span  girder  can 
be  moulded  separately  and  set  in  place.  This  is  not  a  paramount  feature 
in  highway  bridges,  but  it  is  often  all-important  in  railway  structures. 

Comparing  simple  girders  and  continuous  ones  of  three  or  more  spans, 
the  following  general  observations  may  be  made: 

If  there  is  no  T-beam  action,  the  simple  spans  will  be  the  more  expen- 
sive; because  the  section  will  be  determined  by  the  moment  at  mid-span  in 
the  simple  girder,  and  this  is  greater  than  any  of  the  moments  of  the  con- 
tinuous girders.  Again,  higher  unit  stresses  than  ordinary  are  allowed 
over  the  supports  of  continuous  girders.  For  the  T-section,  if  the  bottoms 
are  straight,  the  continuous  type  will  be  the  more  expensive,  having  more 
concrete  and  more  steel  than  the  simple  type.  But  if  the  bottoms  of  all 
girders  are  cur-ved,  the  continuous  girders  will  be  the  cheaper,  there  being 
decidedly  less  concrete  required  for  them.  When  the  bottoms  are  straight 
for  simple-span  girders  and  are  cui^ed  for  continuous  girders,  the  curves  on 
page  1323  of  "Bridge  Engineering"  indicate  the  relationships.     It  will  be 


222  ECONOMICS   OF  BRIDGEWOEK  Chapter  XXV 

noted  therefrom  that  for  hght  loads  the  simple  spans  have  less  concrete, 
and  that  for  heavy  girders  there  is  but  little  difference  in  the  concrete 
quantities,  excepting  that  for  exceedinglj^-heavj^,  long-span  girders  the 
continuous  type  is  the  lighter.  There  is  always  more  steel  required  for  the 
continuous  type  than  for  the  non-continuous  one. 

From  the  foregoing  remarks  it  is  evident  that  shnple-span  girders  are 
generally  cheaper  than  the  continuous  ones.  It  will  be  found,  however, 
that  the  bents  or  other  supports  are  cheaper  for  continuous  girders  than  for 
simple  ones,  and  that  floor  joints  in  simple  spans  are  expensive,  also  that 
the  continuous  girders  give  a  solid,  monolithic  structure.  The  continuous- 
girder  construction  is  very  generally  used  in  highway  bridges;  but  the 
railway  companies  have  adopted  as  standard  the  simple-girder  type.  How- 
ever, nearly  all  railway  concrete-bridges  up  to  the  present  have  been  of 
soUd-slab  construction,  rather  than  of  that  of  the  slab-girder. 

The  foregoing  comparisons  are  based  upon  girders  in  which  the  rein- 
forcement was  liberally  proportioned  for  positive  moments,  negative 
moments,  and  shears,  making  full  provision  for  impact  and  a  small  allow- 
ance for  uncertainties  of  stress  distribution  in  continuous  girders.  It  is 
possible  to  skimp  the  reinforcing  of  concrete  girders  considerably,  and 
this  practice  in  highway  bridgework  is  altogether  too  common.  It  is 
an  evil  that  should  be  stamped  out,  if  not  by  the  engineering  profession, 
then  by  the  laws  of  the  land ;  for  while  it  is  most  reprehensible  to  skin  a 
steel  bridge  in  which  the  skinning  cannot  be  hidden  from  the  expert  eye, 
it  is  criminal  to  trim  down  to  dangerous  limits  of  strength  a  reinforced- 
concrete  structure  in  which  the  flaws  and  weaknesses  are  buried  out  of 
sight. 

The  character  of  the  foundations  should  be  duly  considered  in  deciding 
between  simple  and  continuous  girders;  for,  if  there  is  danger  of  settle- 
ment, the  simple-girder  type  is  far  preferable — in  fact,  it  is  obhgatory. 

The  balanced-cantilever  type  of  girder  is  beginning  to  be  used,  each 
monolithic  unit  consisting  of  a  pier  and  two  half-spans.  In  this  the 
foundation  pressure  is  centric  for  dead  load  and  for  hve  load  over  the  two 
arms;  but  with  the  latter  loading  on  one  arm  only,  the  pressure  en  the 
base  is  decidedly  eccentric,  subjecting  the  pier  shaft  to  bending.  This 
type  of  layout  permits  of  a  very  shallow  depth  at  the  center  of  the  span, 
and  is  thus  specially  applicable  to  long  spans,  where  the  weight  of  the 
concrete  in  the  central  portion  of  either  simi)le  or  continuous  girders  is 
an  important  factor.  The  balanced-cantilever  girder  usuall.v  shows  for 
the  superstructure  a  small  economy  over  either  the  simple  oi-  the  con- 
tinuous girder  for  short  spans  and  a  larger  saving  for  long  ones.  The 
substru(;tui-e,  though,  is  always  more  expensive,  as  it  has  to  be  designed 
for  the  unbalanced  load  on  one  arm.  If  the  live  load  is  small  in  com- 
parison with  the  dead  load,  this  increase  in  sub-structure  cost  is  not  great; 
but  otherwise  it  is  so  large  as  to  outweigh  the  economy  in  the  girders 
themselves.     This  type  of  layout  should  not  be  used  on  soft  foundations 


ECONOMICS   OF   KEINFORCED-CONCRETE   BRIDGES  223 

or  with  pile  bearings  when  the  Hve  load  is  comparatively  great,  on  account 
of  the  tendency  to  rock  the  piers.  Where  the  ends  of  the  arms  come 
together  it  is  necessary  to  insert  a  detail  that  will  take  up  shear  but  not 
moment;  for,  otherwise,  there  would  be  a  sudden  break  in  the  grade  that 
might  give  serious  trouble.  In  the  author's  opinion  this  type  is  never 
suitable  for  carrying  steam-railwg^y  loadings  and  is  none  too  good  for 
electric-railway  structures,  although  satisfactory  enough  for  highway 
bridges.  In  order  to  determine  for  any  case  the  relative  economy  of 
cantilever  and  ordinary  types,  estimates  for  both  superstructure  and  sub- 
structure will  have  to  be  made. 

Columns 

Columns  are  generally  square  or  rectangular  in  cross-section  for  con- 
structive and  aesthetic  reasons.  A  round  or  octagonal  column  is  really 
a  better  structural  member;  and,  if  the  lines  of  the  bridge  are  worked  out 
in  accordance  with  it,  there  should  seldom  be  any  difficulty  about  the  matter 
of  appearance.  A  round  column  can  be  hooped  or  banded  better  than 
any  other  type.  Frequently,  for  the  sake  of  appearance,  the  size  of  a 
column  must  be  made  greater  than  that  necessitated  by  theoretical  require- 
ments. 

Footings 

Footings  may  be  either  plain  or  reinforced;  and  the  question  as  to 
which  style  to  adopt  is  one  solely  of  economics,  because,  as  they  are  buried 
out  of  sight,  the  consideration  of  aesthetics  will  not  apply.  If  the  area  of 
the  footing  is  but  little  larger  than  that  of  the  column  supported,  plain 
concrete  wiU  be  the  cheaper;  while  for  a  spread  foundation  the  reinforced 
type  will  nearly  always  be  found  more  economical.  If  a  footing  has  to 
be  poured  under  water,  plain  concrete  should  invariably  be  employed; 
and  in  wet-excavation  work  in  general  it  is  preferable,  because  it  is  often 
difficult  to  prepare  the  bottom  of  the  pit  properly,  and  to  stop  absolutely 
the  flow  of  water  from  below.  Such  a  flow  is  liable  to  wash  out  the  cement 
from  the  lower  part  of  the  footing;  and  thus  it  would  destroy  most  of  the 
value  of  the  reinforcing. 

Plain  footings  are  made  of  1:3:5  concrete  or  sometimes  1:3:6; 
but  the  latter,  in  the  author's  opinion,  is  too  weak.  The  use  of  1  :  2  :  4 
concrete  permits  thinner  footings,  but  this  is  not  of  much  importance 
when  plain-concrete  bases  are  used. 

Highway  Girder  Bridges 

In  respect  to  the  economics  of  girder  bridges  resting  on  columns,  the 
following  points  must  be  considered: 

First.     The  panel  length,  when  cross-girders  are  employed. 
Second.     The  number  and  spacing  of  the  longitudinal  girders. 
Third.     The  number  of  columns  per  bent. 


224  ECONOMICS   or  BRIDGEWORK  Chapter  XXV 

Fourth.     The  span  length. 

Fifth.     The  use  of  reinforced  concrete  piles  to  carry  the  footings. 

The  panel  length  adopted  is  usually  not  of  great  unportance  from  the 
standpoint  of  economy.  Lengths  of  from  eight  to  ten  feet  are  generally 
employed;  but  a  considerable  variation  from  these  values  will  cause 
httle  change  in  the  combined  cost  of  the  slabs  and  cross-girders.  A 
reduction  in  concrete  quantities  can  frequently  be  effected  by  using  long 
panels,  and  by  carrying  the  slabs  on  short  stringers  supported  by  the  floor- 
beams;  but  the  extra  form  work  required  will  generally  overbalance 
this  saving  in  volume. 

The  number  and  spacing  of  the  longitudinal  girders  will  depend  upon 
the  width  and  the  height  of  the  structure,  the  span-length,  and  the  load 
to  be  carried.  For  a  high  structure  in  which  the  economic  span-length  is 
fairly  great,  it  will  nearly  always  be  found  best  to  employ  two  lines  of 
girders,  the  spacing  thereof  being  equal  to  about  five-eighths  of  the  total 
width  of  the  structure;  but  for  bridges  much  over  sixty  (60)  feet  wide  the 
use  of  three  or  even  four  lines  may  be  preferable.  The  slab  in  such  struc- 
tures is  carried  on  cross-girders  and  cantilever-beams.  For  a  low  bridge  in 
which  the  economic  span  length  is  short,  it  will  generally  be  the  cheapest 
to  omit  the  cross-girders,  except  at  the  bents,  and  to  employ  several 
lines  of  longitudinal  girders.  The  wider  the  structure,  the  more  hkely 
will  this  arrangement  prove  to  be  economical;  and  very  heavy"  loads  also 
favor  its  adoption.  For  a  structure  in  which  the  span-length  is  from  one- 
half  to  two-thirds  of  the  width,  it  will  usually  make  httle  difference  which 
of  the  two  types  is  adopted,  unless  the  height  is  rather  large;  and  even  in 
extreme  cases  the  variation  between  the  two  is  not  likely  to  exceed  ten 
per  cent.  Ordinarily,  it  will  be  found  more  desirable  to  use  two  lines  of 
girders,  with  cross-girders  and  cantilevers  about  eight  or  ten  feet  centers. 
The  proper  number  of  columns  per  bent  depends  on  the  number  of 
longitudinal  girders.  When  there  are  only  two  Hues,  two  columns  will, 
of  course,  be  employed.  Wlien  there  are  several  lines  of  girders,  there 
should  generally  be  one  column  per  girder  in  low  structures,  and  two 
columns  per  bent  in  higher  ones.  In  this  latter  case  a  heavy  cross-girder 
will  be  required  at  each  bent  to  carry  the  longitudinal  girders. 

The  economic  span-length  is  affected  by  the  height  and  the  load,  being 
larger  for  greater  heights  and  smaller  for  heavier  loads.  An  approxunate 
value  thereof  is  given  by  the  formula, 

in  which  i  =  economic  span  length  in  feet,  measured  from  center  to  center 
of  supports, 
w  =  load  in  pounds  per  lineal  foot  of  girder  (excluding  its  own 
weight) , 
and  h  =  fixed  height  of  structure  in  feet. 


ECONOMICS   OF   REINFORCED-CONCEETE    BRIDGES  225 

The  quantity  h  represents  in  any  given  case  the  height  which  is  fixed,  such 
as  the  height  from  grade  to  top  of  footing,  height  from  grade  to  bottom  of 
footing,  height  from  underside  of  girder  to  top  of  footing,  or  height  from 
underside  of  girder  to  bottom  of  footing,  as  the  case  may  be.  There  is 
always  a  considerable  range  of  lengths  for  which  the  quantities  remain 
nearly  constant.  The  formula  gives  values  a  trifle  greater  than  those  for 
which  the  quantities  are  a  minimum,  since  the  use  of  heavier  sections  will 
reduce  slightly  the  unit  costs  of  the  concrete. 

Reinforced-concrete  piles  should  be  used  under  footings  when  a  suitable 
foundation  is  to  be  found  only  at  a  considerable  depth,  or  v/hen  a  very 
large  footing-area  would  be  required  in  order  to  reduce  the  pressures  to 
a  proper  amount.  A  comparison  must  be  made  for  each  case  as  it  arises, 
allowing  properly  for  the  costs  of  the  column  shaft,  the  footing,  the  piles, 
and  the  excavation.     This  latter  item  must  not  be  overlooked. 

The  curves  of  Figs.  5Qt  to  5Qy,  inclusive,  of  ''Bridge  Engineering," 
will  be  found  of  great  value  in  studying  the  questions  of  economy  of  rein- 
forced-concrete-girder  bridges,  as  most  of  the  points  involved  can  be  settled 
directly  thereby. 

Arch  Bridges 
Economic  Rise  with  Span -Length    Unchanged 

The  economics  of  arch  bridges  are  much  more  complicated  than  those 
of  girder  bridges.  The  important  factors  are  the  costs  of  the  arch  ribs  and 
those  of  the  piers  or  abutments ;  and  the  main  economic  point  to  determine 
is  that  of  ratio  of  rise  to  span-length.  For  any  fixed  span-length,  the 
greater  the  rise,  up  to  a  limit  of  one-third  of  the  opening,  the  smaller  will  be 
the  cost  of  both  arch-ribs  and  piers.  By  increasing  it  further,  up  to  the 
limit  of  one-half  of  the  opening,  the  cost  of  the  rib  will  be  but  little  aug- 
mented, and  the  cost  of  the  pier  above  the  springing  will  be  increased,  while 
that  of  the  portion  thereof  below  the  same  will  be  reduced.  If  the  increase 
in  rise  is  secured  by  lowering  the  springings,  the  greater  the  rise  the 
greater  the  economy  of  material  and  cost;  but  if  the  increase  must  be 
secured  by  raising  the  grade,  the  springing  remaining  at  a  fixed  elevation, 
it  will  rarely  be  economical  to  increase  the  rise  above  the  Kmit  of  one- 
third  of  the  opening.  The  exact  limit  in  any  case  will  depend  upon  the 
distance  from  the  springing  to  the  bottom  of  the  base,  and  upon  the  mass- 
iveness  of  the  pier-shafts  above  the  springing;  also  upon  the  spans  of  the 
arch-ribs  resting  on  the  pier,  and  upon  the  character  of  the  substructure 
employed.  If  the  springing  is  but  little  above  the  top  of  the  base,  a 
comparatively-low  rise  will  be  economic. 

If  the  pier  carries  two  arch-spans  of  the  same  length,  and  if  the  live  loads 
are  small  as  compared  with  the  dead  loads,  a  low  ratio  of  rise  to  span-length 
will  be  economic.  On  the  other  hand,  if  the  distance  from  the  springing 
to  the  bottom  of  the  base  be  great,  the  live  load  large  as  compared  with  the 


226  ECONOMICS   OF   BRTDGEWORK:  Chapter  XXV 

dead  load,  the  two  adjacent  arch  spans  of  different  lengths  (or,  still  more 
important,  if  there  be  only  one  arch),  and  the  substructure  work  expensive 
or  the  foundation  of  low  bearing-value,  the  ratio  of  rise  to  span  length 
should  be  large. 

Frequently  an  arch  abutment  retains  a  fill,  in  which  case  a  veiy  low  rise 
is  likely  to  be  economic,  in  order  that  the  larger  thrust  of  the  rib  may  oppose 
the  earth-thrust  on  the  abutment.  In  such  an  event  it  may  be  economic 
to  make  the  springing  higher.  This  is  the  only  exception  to  the  general 
rule  that,  for  maximum  economy,  the  springing  should  be  placed  as  low  as 
clearances,  waterway  requirements,  or  due  consideration  of  aesthetics  will 
permit. 

Economic  Span-Length  with  Rise  Unchanged 

In  most  instances  there  is  Httle  chance  to  vary  either  the  grade  or  the 
elevations  of  the  springings  to  any  great  extent;  hence  the  principal  eco- 
nomic problem  is  the  determination  of  the  best  span-length.  The  prin- 
cipal factors  to  be  considered  are  the  following: 

A.  The  rise  of  the  arch. 

B.  The  distance  from  springing  to  bottom  of  base. 

C.  The  character  of  the  substructure  work. 

D.  The  massiveness  or  hghtness  of  the  piers,  determined  from  the 

aesthetic  viewpoint. 

E.  The  ratio  of  Uve  load  to  dead  load.   , 

F.  The  type  of  arch-ring — whether  solid-barrel  or  two  or  more 

separate  ribs. 

G.  The  equality  or  inequaUty  of  lengths  of  adjacent  spans. 

H.     Arbitrary  requirements  fixing  clearances  of  ribs  or  positions  of 

piers. 
I.     Other  special  conditions. 

The  rise  of  the  arch  is  evidently  of  paramount  importance;  because 
the  greater  it  is  the  greater  will  be  the  economic  length  of  span. 

The  distance  from  springing  to  bottom  of  base  is  another  very  impor- 
tant factor.  In  general,  it  may  be  stated  that,  for  ribbed  arches,  when  the 
adjoining  spans  are  of  equal  length  and  when  the  springings  are  but  a  short 
distance  above  the  bottom  of  the  base,  a  ratio  of  rise  to  span-length  of  one- 
third  or  even  le:3s  will  be  quite  economic;  while,  if  the  said  springings  are  a 
considerable  distance  above  the  said  bottom,  a  ratio  of  one-half  wiU  be 
better.  Generally  speaking,  it  may  be  said  that  low  ratios  of  rise  to  span 
are  more  pleasing  to  the  eye  than  higiier  ones,  so  that  the  adoption  of 
longer  spans  is  preferable  from  the  aesthetic  standpoint.  Also  longer 
spans  involve  larger  members,  and  consequently  lower  unit  costs,  so  that 
the  economic  span-length  is  somewhat  greater  than  that  which  gives  mini- 
mum quantities  of  materials. 


ECONOMICS   OF   REINFORCED-CONCRETE   BRIDGES  227 

Difficult  foundations  favor  long  spans,  not  only  because  of  the  reduc- 
tion in  the  number  of  piers  but  also  because  the  unit  costs  for  small  piers 
are  much  higher  than  those  for  large  ones.  On  the  other  hand,  if  the 
foundations  are  very  deep,  the  effect  of  unbalanced  thrusts  becomes  of 
great  importance;  and  this  favors  shorter  spans.  Poor  foundation  con- 
ditions also  mihtate  for  shorter  spans,  as  do  invariably  pile  foundations. 

If  it  be  decided  for  the  sake  of  appearance  to  make  the  piers  heavy  and 
massive,  this  will  tend  towards  greater  span-length;  because,  in  that 
case,  up  to  a  certain  limit,  an  increase  of  span  will  augment  the  size  of 
each  individual  pier  but  little,  if  any.  It  will  rarely  pay  to  reduce  the 
span-length,  if  such  reduction  will  not  decrease  the  size  of  the  pier 
or  piers. 

Light  live  loads  in  proportion  to  the  dead  loads  tend,  for  economy, 
towards  the  adoption  of  longer  spans,  especially  when  the  adjoining  spans 
are  of  the  same  length.  With  such  light  live  loads  the  economic  span- 
length  is  not  greatly  affected  by  the  distance  from  springing  to  bottom  of 
base.  When  a  pier  carries  one  arch  span  only,  the  ratio  of  hve  load  to 
dead  load  is  of  much  smaller  importance  than  it  is  in  the  case  where  there 
is  a  succession  of  spans. 

The  type  of  arch  ring,  whether  it  be  of  one  solid-barrel  or  of  two  or 
more  arch  ribs,  often  affects  materially  the  economic  span-length,  but  to 
what  extent  it  is  difficult  to  predict  in  advance  of  designing  and  esti- 
mating. The  piers  of  the  solid-barrel  type  are  generally  more  expensive 
than  those  of  the  ribbed  type,  as  are  also  the  arches;  but  in  most  cases 
the  piers  are  comparatively  the  more  expensive;  and  this  favors  the 
employment  of  longer  spans.  Also,  it  wiU  frequently  be  found  that 
increasing  the  span-length  will  augment  but  slightly  the  quantities  in  the 
arch  rings  of  the  solid-barrel  type — which  also  favors  longer  spans.  The 
economic  ratio  of  rise  to  span-length  for  solid-barrel  arches  may  generally 
be  taken  at  0.25,  varying,  of  course,  with  the  other  factors  previously  dis- 
cussed. The  foregoing  conclusion  may  seem  to  be  in  contradiction  to 
the  well-known  fact  that  long  spans  are  nearly  always  of  the  ribbed  type. 
This,  however,  is  because  the  solid-barreled  arch  is  generally  used  for  low 
rises,  which  necessarily  means  comparatively  short  spans,  while  the  open- 
ribbed  arches  are  employed  for  nearly  all  arch  structures  of  high  rise. 
The  comparative  economics  of  these  two  types  will  be  discussed  later  in 
this  chapter. 

When  adjoining  spans  must  be  unequal,  the  inequality,  for  economy's 
sake,  should  be  made  as  small  as  practicable.  This  is  very  important  if 
the  springings  are  far  above  the  base;  but  is  of  small  consequence  if  they 
are  not.  If  the  springing  of  the  smaller  arch  can  be  located  well  above 
that  of  the  larger  one,  it  may  be  possible  so  to  adjust  the  spans  and  rises 
that  there  shall  be  very  little  eccentricity  of  pressure  on  the  base,  in  which 
case  the  pier  will  not  be  much  more  expensive  than  it  would  have  been 
had  the  adjacent  spans  been  of  equal  length.     The  appearance  of  the  piers 


228  ECONOMICS  OF  BRIDGEWORK  Chapter  XXV 

will  demand  special  study,  if  the  springings  are  located  at  different  ele- 
vations; otherwise,  the  principles  of  aesthetics  are  likely  to  be  violated. 

The  influence  of  earth-thrust  on  an  arch  abutment  has  already  been 
mentioned.  Where  such  thrust  exists,  it  will  favor  the  use  of  longer  spans, 
in  order  that  the  larger  arch-thrust  may  counterbalance  the  said  earth- 
thrust.  In  a  long  bridge  of  many  spans,  the  abutments  will  not  cut 
much  figure;  but  if  only  two  or  three  spans  are  to  be  adopted,  they  may 
be  of  more  importance  than  the  intermediate  piers.  If  there  is  no  earth- 
thrust  on  the  abutment,  its  cost  will  augment  as  the  span-length  increases; 
but  if  there  is  such  a  thrust,  the  cost  may  reduce  when  the  span-length  is 
made  greater. 

In  many  layouts  the  positions  and  even  the  sizes  of  certain  piers  are 
fixed,  and  specified  clearances  (both  horizontal  and  vertical)  must  be 
maintained  under  certain  of  the  spans.  These  conditions,  of  course,  must 
be  taken  as  a  basis,  and  the  layout  adapted  to  suit  them.  Special  govern- 
ing conditions  must  often  be  observed,  such  as  the  character  of  the  sur- 
roundings, the  relative  importance  of  aesthetics  and  cost,  or  the  adoption 
of  some  special  architectural  treatment. 

In  a  discussion  of  economic  span-lengths  of  arch  bridges  it  is  imprac- 
ticable to  give  exact  figures,  for  there  are  too  many  variables  concerned. 
Whenever  there  is  any  choice,  it  wiU  be  necessary  to  make  preliminary 
designs  for  at  least  two  span-lengths;  and,  if  one  of  these  proves  to  be 
somewhat  cheaper  than  the  other,  a  third  length  should  be  figured.  There 
is  no  other  way  to  ensure  that  the  truly  economic  length  has  been  selected, 
unless  it  happens  that  the  figures  can  be  compared  with  those  for  a  very 
similar  structure. 

Comparison  of  Solid-Spandrel  versus  Open-Spandrel  and  Solid- 
Barrel  versus  Ribbed  Structures 

Arch-spans  can  be  divided  into  two  general  classes,  solid-spandrel  and 
open-spandrel.  In  the  first  form  the  arch-rib  must  be  solid,  while  in  the 
second  it  may  be  either  solid  or  ribbed.  Considering  the  two  solid-barrel 
types,  the  filled-spandrel  has  no  floor-system  or  cross  walls,  but  instead 
an  earth  fill  between  the  spandrel-walls.  For  very  low  rises  the  walls  and 
filling  are  cheaper  than  the  floor-system  and  columns;  but  for  high  rises 
the  reverse  is  true.  The  great  weight  of  the  filling  makes  the  piers  expen- 
sive in  the  cases  of  pile  foundations  and  bearings  upon  comparatively 
soft  soil.  The  spandrel-filled  arch  is  often  used  on  railroads  when  it  is 
not  the  most  economic  type,  in  order  thnt  the  weight  and  inertia  of  the 
filling  may  absorb  the  impact  of  moving  trains. 

In  highway  structures,  the  open-spandrel  type  is  generally  preferred 
to  the  filled  type,  for  various  good  and  economic  reasons,  among  which 
may  be  mentioned  the  fact  that,  with  the  latter  type,  it  will  be  found 
desirable,  for  the  sake  of  appearance,  to  make  the  ring  the  full  width  of  the 


ECONOMICS   OF   REINFORCED-CONCRETE   BRIDGES  229 

deck;  whereas  for  the  former  type  it  will  be  satisfactory  to  carry  a  part  of 
the  deck  on  cantilevers.  The  consequent  narrowing  of  the  arch-rings 
and  shortening  of  the  piers  involve  quite  a  saving  in  cost. 

Comparing,  in  open-spandrel  structures,  the  solid-barrel  type  and  the 
ribbed  type,  it  will  be  found  that  the  latter  is  cheaper,  except  in  the  case  of 
very  low  ratios  of  rise  to  span-length.  In  the  solid-barrel  type  there  is 
one  wide,  rather-thin  ring  carried  on  a  wide,  comparatively-thin  pier;  while 
in  the  ribbed  type  there  are  two  or  more  thicker  and  rather-narrow  ribs, 
carried  on  piers  which  must  be  somewhat  wide  as  seen  in  side  elevation, 
there  usually  being  a  separate  shaft  for  each  hne  of  ribs.  For  arches  of 
considerable  rise  in  which  the  Uve  load  moments  are  the  only  ones  of  impor- 
tance, the  thick,  narrow  rib  is  much  the  cheaper;  but,  as  the  rise  is  reduced, 
temperature  and  arch-shortening  stresses  increase  in  importance,  and  it 
becomes  more  economical  to  reduce  the  thickness  and  make  each  rib  wider, 
until  eventually  the  sohd-barrel  rib  is  reached.  For  any  special  case,  com- 
parison can  be  made  by  means  of  the  curves  on  pages  1332  and  1333  of 
"Bridge  Engineering."  It  must  not  be  forgotten  that,  with  the  ribbed 
type,  cross-braces  between  the  ribs  are  generally  necessary.  The  type  of 
pier  required  is  also  important.  If  a  separate  shaft  can  be  used  for  each 
line  of  ribs,  the  ribbed  type  will  usually  be  the  more  economical;  but  in 
many  cases,  as  in  most  rivers,  solid  pier-shafts  must  be  employed  in  any 
event.  Frequently,  in  river  crossings,  the  springings  are  located  below  the 
high-water  line;  and  the  adoption  of  solid  barrels  then  becomes  almost 
imperative. 

Hingeless  and  Three-Hinged  Arches 

Comparing  the  hingeless  and  the  three-hinged  types  for  reinforced- 
concrete  arch-bridges,  it  will  be  found  that  the  latter  is  cheaper  for  low 
rises,  and  the  former  for  high  ones.  The  principal  objection  to  the  three- 
hinged  type  is  its  awkward  appearance,  due  to  the  fact  that  it  is  thicker  in 
the  haunch  than  at  the  springing  line;  and  since  the  concrete-arch  bridge  is 
often  selected  from  aesthetic  considerations,  this  is  an  important  matter. 
If  the  three-hinged  rib  be  thickened  at  the  springing,  in  order  to  make  its 
appearance  satisfactory,  it  will  rarely,  if  ever,  prove  to  be  cheaper  than  the 
hingeless  type. 

Arch  with  Steel  Bottom  Chords 

An  unusual  economic  problem  arose  in  the  design  of  the  author's 
Twelfth  Street  Trafficway  Viaduct  in  Kansas  City,  Mo.  This  is  a  double- 
deck,  reinforced-concrete-girder  structure;  but  there  was  one  portion  of 
it  where  a  134-foot  span  was  required  over  some  railroad  tracks.  An  arch 
span  was  adopted;  but  the  springings  were  high  above  the  foundations, 
which  were  on  piles;  and  the  area  allowable  for  the  piers  was  restricted  by 
other  tracks.     The  question  of  what  to  do  was  finally  solved  by  putting  in 


230  ECONOMICS   OF  BRIDGEWOEK  Chapter  XXV 

encased  bottom  chords  of  eye-bars  at  the  elevation  of  the  lower  deck,  so  as 
to  take  up  the  arch  thrusts.  The  available  clearance  was  very  small;  so 
that  the  floor-beams  of  the  lower  deck  had  to  be  made  of  steel  I-beams 
encased  in  concrete  and  riveted  to  steel  hangers,  also  encased. 

Reinforced-Concrete  Trestles  for  Steam  Railways 

A  number  of  reinf orced-concrete  trestles  have  been  built  of  late  years  for 
steam-railways.  The  usual  type  for  river  crossings  has  been  sohd-concrete 
slabs  on  concrete  piles.  The  economic  span-lengths  for  such  trestles 
are  very  short,  usually  from  ten  (10)  to  fifteen  (15)  feet;  but  most  of  the 
structures  have  had  spans  of  fifteen  (15)  or  twenty  (20)  feet  on  account  of 
waterway  requirements.  Solid  slabs  have  also  been  used  extensively  for 
grade-crossing-elimination  work  in  cities,  the  substructure  generally  con- 
sisting of  either  soUd  cross-walls  or  cross-girders  resting  on  a  row  of  small 
columns  carried  on  a  continuous  footing.  The  economic  span-lengths  for 
such  structures  are  a  little  greater  than  those  for  the  slab-pile-trestles;  but 
this  economic  question  is  of  very  small  importance,  since  the  span-lengths 
are  generally  fixed  definitely  by  other  considerations. 

The  slabs  for  most  of  these  trestles  have  been  separately  moulded  and 
afterwards  set  into  place  by  derrick  cars  or  locomotive  cranes.  In  some 
cases  this  was  the  cheapest  possible  method  of  construction;  but  in  others 
the  need  for  maintenance  of  traffic  demanded  it.  In  many  cases  also  the 
headroom  was  limited,  and  falsework  beneath  was  not  permissible. 

For  the  purpose  of  determining  the  economics  involved,  the  author  has 
had  made  in  his  offices  during  the  last  three  or  four  years  a  large  number  of 
estimates  for  steam-railway,  reinf  orced-concrete  trestles  of  the  slab-girder 
type,  for  span-lengths  varying  from  twenty  (20)  to  fifty  (50)  feet,  and  for 
heights  varying  from  twenty  (20)  to  sixty  (60)  feet,  measuring  from  base 
of  rail  to  bottoms  of  footings.  Both  sunple  and  continuous  girders  have 
been  computed,  the  former  proving  somewhat  the  cheaper.  The  substruc- 
ture considered  consists  of  bents  composed  of  two  battered  columns  with  a 
cross-girder  at  the  top,  the  columns  being  supported  by  either  one  con- 
tinuous footing  or  two  separate  footings.  For  the  higher  trestles  it  proved 
to  be  economical  to  use  longitudinal  struts  between  columns  in  alternate 
spans,  thus  making  a  succession  of  towers  with  a  single  span  between  each 
of  them.  The  economic  span-length  for  such  trestles  varies  from  one-half 
to  six-tenths  of  the  height. 

In  the  second  edition  of  "Bridge  Engineering"  (fourth  thousand),  which 
will  probably  be  issued  in  1922,  there  will  be  a  lengthy  Appendix  for  the 
purpose  of  recording  the  results  of  all  of  the  author's  studies  (excepting  the 
economic  ones  reproduced  in  this  treatise)  on  the  subject  of  bridges  made 
since  July,  1916,  when  the  first  edition  of  that  work  appeared.  The  said 
Appendix  will  contain  an  extensive  series  of  diagrams  giving  curves  of 
quantities  for  diffei-ent  types  of  steam-railway,  reinforced-concrctc  trestles. 


ECONOMICS   OF   REINFORCED-CONCEETE   BRIDGES  231 

Comparing  such  structures  with  those  composed  of  steel  girders  carrying 
ballasted  decks  on  concrete  slabs,  there  is  very  little  difference  in  cost,  the 
reinforced-concrete  trestles,  pure-and-simple,  being  a  trifle  cheaper  for 
twenty-foot  spans  and  a  little  more  expensive  for  fifty-foot  spans.  But  if 
the  steel  girders  are  encased  in  concrete,  the  reinforced-concrete  trestle  will 
always  be  found  the  cheaper. 

Retaining  Walls 

Reinforced-concrete  retaining  walls  show  a  small  saving  over  plain-con- 
crete ones  for  even  small  heights.  However,  it  is  better  to  use  plain  con- 
crete up  to  heights  of  ten  (10)  feet,  measuring  from  bottom  of  footing  to 
grade,  as  the  section  of  a  low  reinforced-concrete  retaining  wall  is  too  small, 
for  the  reason  that  a  certain  amount  of  massiveness  is  necessary  in  such 
constructions. 

In  respect  to  the  economics  of  cantilevered  and  counterforted  walls, 
the  former  type  is  the  cheaper  up  to  about  twenty  or  twenty-five-foot 
heights,  above  which  limit  the  latter  type  is  the  more  economic.  The  dis- 
cussion of  ''Footings"  previously  given  in  this  chapter  will  apply  to  the 
footings  of  retaining  walls. 


CHAPTER  XXVI 

ECONOMICS   OF  STEEL  ARCH-BRIDGES 

For  some  twenty-five  or  thirty  years  American  bridge  engineers  have 
been  sadly  in  need  of  reUable  information  concerning  certain  fundamental 
economic  functions  of  steel  arch-bridges,  and  especially  the  relative  costs 
of  such  structures  in  comparison  with  the  corresponding  truss  bridges. 
The  want  of  such  information  has  resulted  in  the  failure  of  American 
engineers  to  develop  the  steel  arch  and  to  use  it  in  places  where  it  would 
be  both  m-ore  economic  and  more  aesthetic  than  the  simple-truss  bridge. 
Wherever  the  governing  conditions  of  crossing  are  suitable  for  an  arch 
structure,  that  type  of  bridge  is  to  be  preferred;  for,  as  we  now  know,  the 
arch,  in  all  places  where  its  use  is  really  justified,  is  less  expensive  than  the 
truss  bridge. 

For  two  decades  or  more,  the  author  had  been  urging  the  engineering 
profession  to  make  certain  investigations  which  would  settle  for  all  time 
every  uncertainty  concerning  the  economics  of  designing  steel-arch  bridges, 
as  well  as  the  relative  costs  of  these  structures  in  comparison  with  the  cor- 
responding truss  bridges.  As  long  ago  as  1897,  when  he  wrote  "De 
Pontibus,"  he  appealed  to  the  engineering  profession  as  follows: 

In  concluding  this  chapter,  the  author  desires  to  call  attention  to  the  fact  that 
there  is  still  a  great  deal  to  be  learned  about  the  designing  of  arches;  and  to  suggest 
that  some  professor  of  civil  engineering,  who  is  well  posted  on  bridge  designing  and 
who  has  time  to  spare,  could  spend  several  months  to  the  great  advantage  of 
the  engineering  profession  in  determining  the  proper  relations  of  span-lengths,  rise, 
arch  depth,  width  between  exterior  arches,  etc.,  for  the  varous  styles  of  arch,  and  in 
ascertaining  the  relative  economies  of  the  latter. 

During  the  eighteen  years  which  elapsed  between  the  issuing  of  ''De 
Pontibus"  and  its  successor,  "Bridge  Engineering,"  the  author  made 
repeated  attempts  to  find  some  bridge  engineer  who  would  be  willing  to 
undertake  the  task' which  he  had  suggested — but  all  to  no  avail;  and  in 
the  last-mentioned  treatise  he  made  another  forcible  appeal  to  the  pro- 
fession to  undertake  the  requisite  investigations,  speaking  as  follows: 

"  For  many  years  the  author  has  been  endeavoring  to  establish  some 
approximate  relation  between  the  weights  of  metal  per  lineal  foot  for 
trusses  and  laterals  of  arch  bridges  and  those  for  the  corresponding  simple 
truss  bridges;  but  has  met  with  very  little  success.  He  once  submitted 
the  (nuisiion  to  his  brotlier  bridge  specialists  of  America,  but  tlioy  were 
unable  to  throw  any  light  upon  the  subject,  because  their  opportunities  to 

232 


ECONOMICS   OF   STEEL   ARCH-BKIDGES  233 

design  and  build  arch  bridges  had  been  few  and  far  between,  and  because  the 
ratio  of  rise  to  span  has  a  great  effect  upon  the  weight  of  metal  in  an  arch. 
Of  course,  there  is  for  any  span  length  some  economic  value  of  that  ratio ; 
but  it  is  not  yet  known,  and  it  probably  varies  more  or  less  not  only  with 
the  span  but  also  with  the  type  of  construction.  The  only  practicable 
method  of  determining  the  original  question  would  be  to  settle  first  that 
of  the  economic  ratios  of  rise  to  span,  design  a  few  arch  bridges  with  the 
said  ratios,  and  make  the  comparison.  This  would  have  to  be  done  for 
the  solid-rib,  the  braced-rib,  and  the  spandrel-braced  types  to  make  the 
job  complete,  adopting  for  the  first  set  of  curves  the  three-hinged  type, 
and  afterward  modifying  the  results  for  the  other  three  types  of  hinging. 
It  is  evident  that  the  amount  of  work  involved  in  such  an  investigation 
would  be  immense.  It  should  be  clone  by  an  experienced  bridge  designer, 
as  the  results  would  be  worthless  if  obtained  by  any  other  investigator. 
The  author  suggests  that  one  of  his  younger  brother-specialists  undertake 
the  investigation." 

The  result  of  this  appeal,  as  in  all  previous  attempts,  was  absolutely 
nil;  and  in  1917,  despairing  of  ever  being  able  to  induce  anyone  to 
assume  the  obKgation,  the  author  himself  shouldered  the  burden  by 
making,  with  the  aid  of  one  of  his  assistants,  all  the  calculations  needed 
to  determine  every  desired  point,  and  from  the  results  thereof  prepared 
a  paper  on  ''The  Economics  of  Steel  Arch  Bridges,"  which  he  presented 
to  the  American  Society,  of  Civil  Engineers.  As  soon  as  he  learned  of  its 
acceptance  by  the  Publication  Committee,  he  sent  a  circular  letter  to  all 
the  bridge  engineers  in  America  whose  addresses  he  could  obtain,  as  well 
as  to  a  number  of  prominent  engineers  abroad,  inviting  them  to  discuss 
the  paper,  and  enclosing  the  following  synopsis: 

Up  to  the  present  time,  nothing  at  all  certain  has  been  known  concerning  the 
economics  of  steel  arch-bridges,  the  weights  of  metal  required  to  build  them,  or  how 
they  compare  in  cost  with  the  corresponding  steel  truss-bridges. 

The  objects  of  this  paper  and  its  anticipated  discussions  are  to  settle  finally  every 
important  economic  question  that  can  arise  in  the  designing  of  steel  arches;  to  give 
formulae  and  diagrams  for  determining,  with  a  fair  amount  of  accuracy,  the  weights  of 
metal  in  both  arch-bridges  as  a  whole  and  the  arches  themselves;  and  to  indicate  the 
relations  between  the  weights  and  costs  of  arch-bridges  in  comparison  with  those  of 
the  corresponding  truss-bridges. 

There  are  eight  economic  problems  set  for  solution;  and  all  of  them  have  been 
solved — the  first  two  by  employing  certain  formulaj  given  in  "Bridge  Engineering," 
and  the  other  six  by  means  of  a  large  number  of  special  arch-designs  and  the  resulting 
estimates  of  weights  of  metal.  Incidentally,  during  the  investigation  there  have  arisen 
and  been  solved  a  few  minor  questions  which  may  properly  be  termed  side-issues. 
The  computations  have  been  made  for  both  railway  and  highway  arch-bridges;  and 
the  weights  of  -metal  are  plotted  for  both  carbon-steel  and  nickel-steel  structures. 
Several  diagrams  are  given  to  show  the  percentage  effects  of  weight-increase  due  to 
departure  from  economic  conditions. 

The  need  for  the  special  knowledge  concerning  arch-bridges  presented  in  this 
paper  has  been  recognized  during  the  last  three  decades  by  American  structural-steel- 
engineers;    but  the  authors  of  books  on  bridges  (this  author  included)  have  hitherto 


234  ECONOMICS   OF  BRIDGEWORK  Chapter  XXVI 

avoided  the  issue  because  of  the  immense  amount  of  work  involved  in  the  solution  of 
the  various  problems.  The  author  has  tried  of  late  years  on  several  occasions  to  per- 
suade some  of  his  brother  engineers  to  undertake  the  task;  but  not  meeting  with  any 
success,  he  finally  decided  to  do  the  work  himself.  The  results  of  his  efforts  are  here- 
with presented  to  the  members  of  the  Society  with  a  most  earnest  request  for  a  thor- 
ough discussion,  particularly  by  those  who  specialize  in  bridgework. 

The  principal  economic  problems  concerning  the  design  of  steel  arch-bridges 
which  have  been  solved  for  this  paper  are  the  following : 

First.     The  economic  ratio  of  rise  to  span-length. 

Second.     The  economic  depths  for  the  ribs. 

Third.  The  economic  location  for  the  crown-hinge  in  three-hinged,  spandrel-braced 
arches. 

Fourth.  The  ratios  of  weights  of  metal  required  for  the  solid-rib,  th3  braced-rib, 
and  the  spandrel-braced  types. 

Fifth.  The  ratios  of  weights  of  metal  required  for  the  hingeless,  the  two-hinged, 
and  the  three-hinged  types. 

Sixth.  The  economics  involved  by  making  arches  three-hinged  for  the  dead  load 
and  two-hinged  for  the  live  load. 

Seventh.  The  economy  of  the  cantilever-arch  with  suspended  end-spans,  as  com- 
pared with  an  ordinary  arch  and  two  flanking  simple-truss-spans. 

Eighth.  The  ratios  of  weights  of  metal  required  for  certain  portions  of  arch 
bridges  as  compared  with  the  corresponding  portions  of  simple-truss  bridges  of  the  same 
span  and  same  Uve-load-carrying-capacity. 

In  answer  to  this  request,  a  number  of  engineers,  both  at  home  and 
abroad,  discussed  the  paper;  and  their  discussions  have  been  printed  in 
several  copies  of  the  Society's  "Proceedings."  These  discussions  have 
been  thoroughly  analyzed  and  replied  to  in  the  closure  of  the  memoir. 

With  one  exception,  the  discussions  did  not  result  in  the  modification 
of  any  of  the  author's  findings — and  in  that  one  the  change  was  not  serious. 
It  was  pointed  out  by  him  that  the  first  two  problems  were  solved  by  the 
use  of  certain  semi-rational,  semi-empirical  formulae  for  weights  of  metal 
in  arches  established  in  Chapter  XXVI  of  "Bridge  Engineering,"  but  that 
the  other  six  were  settled  by  means  of  actual  computations  of  weights  of 
metal  determined  from  specially-prepared  diagrams  of  stresses  and  sec- 
tional areas  of  main  members. 

Mr.  Charles  Evan  Fowler  in  his  thorough  and  elaborate  discussion, 
including  a  tabulation  of  the  salient  features  and  dimensions  of  one 
hundred  of  the  world's  largest  steel-arch-bridges,  showed  that  the  author's 
finding  for  economic  ratios  of  rise  to  span-length  agreed  fairly  well  with  the 
averages  computed  from  existing  structures,  but  that  his  deduced  economic 
ratio  of  depth  of  arch-ring  to  span-length  did  not;  whereupon  the  author 
agreed  to  settle  this  question  beyond  a  doubt  by  submitting  it  to  the 
incontrovertible  test  of  making  actual  designs  and  estimates  of  weights 
for  arches  of  500-feet  span,  of  economic  ratio  of  rise  to  span-length,  and 
having  regularly-varying  depths  of  arch  ribs,  so  as  to  determine  the  depth 
producing  the  least  weight  of  metal.  This  was  done;  and  the  results  of 
the  special  calculations  were  given  in  the  resume,  which  showed  that,  for 
short-span  railroad  arch-bridges,  the  previous  finding  was  correct,  but  that, 


ECONOMICS   OF   STEEL  ARCH-BRTDGES  235 

for  the  corresponding  long-span  structures,  it  was  somewhat  too  great — • 
also  that  the  conclusion  to  the  effect  that  the  economic  depth  for  arch  ribs 
is  the  same  for  both  railway  and  highway  bridges  is  wrong.  The  reason 
for  the  variation  in  the  two  findings  is  that  the  weight  formulae,  upon  which 
the  first  investigation  was  made,  were  of  too  empirical  a  nature  to  warrant 
their  use  for  an  exact  determination  of  economic  depth  of  arch  rib. 

From  the  original  paper,  the  discussions,  and  the  resume,  the  following 
answers  to  the  set  questions  have  been  reached : 

First.  For  three-hinged  arches  with  the  grade  Une  approximately  tan- 
gent to  the  top  chord  of  the  arch  at  the  crown,  the  average  economic 
ratios  of  rise  to  span-length  are  as  follows : 

Solid-rib  structures 0.2 

Braced-rib  structures 0 .  225 

Spandrel-braced  structures  (with  hinge  above) 0 .  25 

These  values  may  be  either  increased  or  decreased  by  0.025  without 
making  any  material  difference  in  the  economics. 

For  three-hinged,  half -through  arch-bridges,  the  average  economic 
ratios  for  rise  to  span-length  are  as  follows: 

Solid-rib  structures 0 .  225 

Braced-rib  structures 0.3 

For  three-hinged,  high-deck  arch-bridges,  they  are  as  follows : 

SoKd-rib  structures 0 .  25  to  0 .  28 

Braced-rib  structures 0 .  33  to  0 .  38 

For  two-hinged  arches  and  combined  two-hinged  and  three-hinged 
arches,  the  economic  ratios  of  rise  to  span  will  be  practically  the  same  as 
for  three-hinged  structures. 

For  the  hingeless  arch,  a  somewhat  greater  ratio  of  rise  to  span  than 
that  for  the  three-hinged  arch  is  economical.  The  single  test  of  this  made 
for  the  500-ft.  span  indicates  that  the  best  ratio  is  about  0.28  with  low- 
grade  deck,  0.33  for  half-through  arches,  and  0.38  with  high-grade  deck. 

Second.  In  respect  to  solid-rib  arches,  the  question  of  economic 
rib-depth  does  not  arise;  for  the  depth  should  always  be  made  as  great  as 
a  proper  consideration  of  the  section  for  resisting  compression  will  permit, 
and  with  due  regard  to  shipping  restrictions  concerning  limiting  sizes  of 
single  pieces.  For  braced-rib,  three-hinged  arches  in  steam-railroad 
bridges,  the  economic  rib-depth  varies  from  7.8%  of  the  span-length  for 
100-ft.  spans  to  5.3%  thereof  for  1000-ft.  spans;  and  for  highway  bridges 
the  corresponding  variation  is  from  5.8%  to  4.2%,  as  shown  in  Fig.  26a. 

The  effects  on  rib  weights  from  using  uneconomic  rib-depths  in  braced- 
rib  arches  for  both  railway  and  highway  bridges  are  given  in  Fig.  266. 

Third.  It  was  found  for  all  cases  that  the  most  economic  location  for 
the  crown-hinge  in  a  spandrel-braced  arch  is  in  the  top  chord.     In  braced^ 


236 


ECONOMICS   OF   BRIDGEWOEK  Chapter  XXVI 


0.03  . 

0         ,100         200         300        400         500         600         700         800         900       3^00 
Span-  length,  in  Feet, 

Fig.  26a.     Economic  Ratios  of  Depth  of  Arch-Rib  to  Span  Length. 
GS       Q6        df        0.8   ..    0.9  ._;  1.0        U        f.2        15        1.4    .    'S 


V5        06    .     aj^  m         0.9  1.0         //  //         /?         M         15 

^^ahos  of  ffdaaf  Fid  Vepfds  fo  rco/jcmic  Eib  Depf/js 

Fig.  20/;.     Effects  on  Rib-"Weights  from  Using  Uneconomic  Rib-Depths  in  Braced-Rib 

Arches. 


ECONOMICS   OF   STEEL   ARCH-BRIDGES 


237 


rib  and  solid-rib  arches,  however,  the  hinge  should  always  be  placed  at  mid- 
depth,  so  as  to  distribute  properly  the  thrust  over  the  two  chords. 

Fourth.  Comparing  the  economics  of  solid-rib,  braced-rib,  and  span- 
drel-braced arches,  it  was  found  that  the  first  mentioned  is  always  con- 
siderably heavier  than  either  of  the  others;  and,  under  normal  conditions 
of  the  metal  market,  it  is  also  more  expensive.  The  spandrel-braced-arch 
requires  for  long  spans  a  little  more  metal  than  the  braced-rib  arch;  but, 


500  600 

Sran.  in  Feet 


U09 


Fig.  26c. 


Ratio  of  Weights  of  Metal  in  Hingeless  Arches  as  Compared  with  Three- 
Hinged  Arches  for  both  Railway  and  Highway  Bridges. 


in  case  of  cantilevering,  this  would  generally  be  offset  by  the  extra  quan- 
tity of  erection  metal  needed  for  the  braced-rib  structure.  In  short  spans, 
the  spandrel-braced  arch  is  a  trifle  the  lighter. 

Fifth.  Comparing  three-hinged,  two-hinged,  and  hingeless  arches,  it 
was  found  that  the  three-hinged  is  a  little  heavier  than  the  two-hinged, 
but  nearly  always  lighter  than  the  hingeless.  The  variations  in  weight 
among  the  three  types,  however,  are  never  great.  In  Fig.  26c  are  given 
ratios  of  weights  of  metal  in  hingeless  arches  as  compared  with  three- 
hinged  arches  for  both  railway  and  highway  bridges. 


238 


ECONOMICS  OF  bridgework: 


Chapter  XXVI 


Sixth.  The  combination  of  three  liinges  for  dead  load  and  two  hinges 
for  Hve  load  produces  very  httle  sa\dng  over  the  three-hinged  type;  but 
it  adds  materially  to  the  rigidity.  In  the  writer's  opinion,  the  combined 
type  is  preferable  to  any  of  the  others. 

Seventh.  ^Vhen  an  arch  is  flanked  by  other  spans  than  arches,  there  is 
generally  quite  a  httle  economy  involved  by  cantilevering  the  ends  of  the 
arch  and  shortening  the  lengths  of  the  smiple  spans.  The  best  proportions 
for  lengths  of  cantilever  arm  and  suspended  span  to  total  length  of  flanking 
span  are,  respectively,  0.4  and  0.6. 

Eighth.  The  ratios  of  weights  of  arches  to  the  weights  of  the  corre- 
sponding simple  spans  for  both  railway  and  highway  bridges  have  been 
determined  and  plotted.  As  was  anticipated,  the  arch  usually  effects  a 
greater  relative  economy  in  highway  structures  than  in  railway  structures 
of  the  same  span  length;  and  the  longer  the  span  the  greater  alwaj^s  is  the 
proportionate  saving  of  metal.  The  results  of  this  investigation  are  shown 
in  Fig.  2Qd. 

100  1 1 1  N  I M  1 1 1 1 11 1 1 1 1 M  1 1 1 1 1 1 1  n  III  I  iTiTTi  I  rn  1 1 1 1 1 1 1 1  ii  1 1 1 1 1 1  n  n  i  n  1 1 1 1 1 1 1 1 1  n  1 1  rrm-nlOO 


i     60 


600  600 

Span,  in  Feet. 


Fig.  26fZ.  Percentages  to  Apply  to  Weights  of  Metal  in  Trusses  of  Simple-Truss  Spans 
in  Order  to  Find  the  Weights  for  Arch-Ribs  and  the  Superimposed  Colunms,  with 
their  Bracing,  to  Carry  the  Same  Live  Loads. 


In  concluding  his  paper,  the  author  quoted  as  follows  from  "Bridge 
Engineering": 

In  dealing  with  the  comparative  economics  of  arches  and  simple  trusses,  it  must  not 
])('.  forgotten  that  there  are  other  factors  than  mere  weight  of  metal  involved;  for  the 
l)ouMd  i)rice  of  the  manufactun^d  material  is  generally  somewhat  greater  for  the  former, 
a:i(l  sometimes  the  cost  of  erection  also  is  larger.  Again,  the  comparison  of  the  costs 
of  arch  superstructures  and  truss  supetstructurcs  alone  is  not  of  much  importance,  for 


ECONOMICS    OF   STEEL   ARCH-BRIDGES  239 

an  economic  investigation,  to  be  of  any  value,  must  include  both  substructure  and 
superstructure;  and  the  costs  of  the  former  are  likely  to  be  very  different  in  arch  designs 
and  simple-truss  designs  for  any  crossing. 

Some  of  the  solutions  of  the  ^'side  issues"  referred  to  in  the  preceding 
"Synopsis"  are  the  following: 

First.  The  percentages  to  apply  to  weights  of  metal  in  simple-truss 
spans,  in  order  to  find  the  weights  for  arch  ribs  and  the  superimposed  col- 
umns with  their  bracing  to  carry  the  same  live  loads,  are  given  by  the 
following  equations: 

For  steam-railway  structures: 

P-106-0.08.S  [Eq.  1] 

For  electric-railway  structures: 

P  =  93-0.07/Sf  [Eq.  2] 

For  highway  structures 

p^80-0.056*S  [Eq.  3] 

In  these  equations  S  is  the  span-length  in  feet,  and  P  is  the  percentage 
to  apply  to  the  weight  of  metal  in  the  trusses  of  any  simple-truss  bridge,  in 
order  to  ascertain  the  weight  of  metal  in  the  corresponding  arches  and  the 
superimposed  columns  with  their  bracing.  It  must  not  be  forgotten 
that  the  superior  limit  of  S  in  these  equations  is  about  1000-ft.,  which  is  as 
far  as  the  recorded  weights  of  simple-truss  spans  are  carried,  and  that  the 
inferior  limit  is  100-ft.  In  Fig.  26d  are  plotted  curves  giving  the  same 
information  as  that  presented  in  the  three  preceding  equations. 

Second.  It  is  evident  from  the  computations  and  the  resultant  diagrams 
that  the  arch  is  more  economical  for  highway  bridges  and  for  combined 
highway  and  electric-railway  bridges  than  for  steam-railway  structures. 
This  is  because  of  the  smaller  ratio  of  live  load  plus  impact  to  total  load  in 
the  former.  The  larger  the  dead  load  of  the  flooring  and  floor-system,  the 
more  advantageous  is  it  for  the  arch  structure  in  comparison  with  the  truss 
bridge. 

Third.  Based  on  the  numerous  weight  computations  made  specially 
for  the  preparation  of  the  paper,  the  following  formulae  for  weights  of  metal 
in  the  arches  alone,  per  lineal  foot  of  span,  in  arch  bridges  of  the  several 
types,  have  been  established: 

For  Three-Hinged  Arches: 

IFa  =  (0 . 000282D^-0 . 000426L)Z  [Eq.  4] 

For  Two-Hinged  Arches: 

PTa  =  (0 .  000248Z)-l-0 .  000416L)Z  [Eq.  5] 

For  Combined  Two-Hinged  and  Three-Hinged  Arches: 

Wc:  -  (0 .  000282D-I-0 .  000416L)^  [Eq.  6] 


240  ECONOMICS   OF  BRIDGE  WORK  Chapter  XXVI 

For  Hingeless  Arches: 

Fa=(0.000272D+0.000460L)i  lEq.  7] 

These  four  formulae  are  based  on  the  author's  pubhshed  designing  speci- 
fications, which  treat  reversing  -stresses  by  adding  one-haK  of  the  smaller 
stress  to  the  larger  stress  and  proportioning  for  the  sum ;  but  if  the  effect  of 
reversion  is  entirely  ignored,  as  some  engineers  deem  proper,  the;'e  formulae 
will  reduce  to  the  following: 

For  Three-Hinged  Ai'ches: 

W'a  =  (0 .  000292Z)+0 .  000396L)Z  [Eq.  8] 

For  Two-Hinged  Arches 

W'a  =  (0 .  000258Z) + 0 .  000380L)  I  [Eq.  9] 

For  Combined  Two-Hinged  and  Three-Hinged  Arches 

F'a=  (0. 0002921) +0.000380L)Z  [Eq.  10] 

For  Hingeless  Arches 

Tf'a=(0.000270D+0.000398L)^  [Eq.  11] 

In  Equations  (4)  to  (11)  inclusive,  Wa,  or  W'a,  is  the  weight  of  metal, 
in  pounds  per  lineal  foot  of  span,  in  the  arches  of  the  structure;  D  is  the 
dead  load,  in  pounds  per  hneal  foot  of  span;  L  is  the  five  load  plus  impact, 
in  pounds  per  lineal  foot,  used  in  making  the  calculations;  and  I  is  the  span 
length,  in  feet.  These  eight  equations  will  give  fairly  accurate  results 
(slightly  on  the  side  of  safety)  for  ordinary  conditions  which  do  not  vary 
greatly  from  the  theoretically  economic  ones. 

In  computing  the  value  of  L  for  insertion  in  Equations  (4)  to  (11),  inclu- 
sive, the  equivalent  uniform  live  load  and  the  impact  should  be  determined 
for  the  half-span-length. 

Fourth.  From  the  formulae  given  above  for  weights  of  arch  ribs,  some 
interesting  deductions  may  be  drawn.     For  instance,  in  Equation  (4),  viz., 

Wa=^(0. 000282Z)-f  0 .  000426L)Z, 

the  dead  load,  D,  is  composed  of  the  rib  weight,  Wa,  plus  the  weight  of  floor, 
columns,  lateral  system,  etc.,  all  of  which  may  be  grouped  under  the 
symbol,  W',  making  the  equation 

Wa  =  (0 .  000282IFa+0 .  000282Tr'+0 .  000426L)Z 

Solving  this  gives 

_  (0 .  000282F'-F0 .  000426L)? 
^°  ~  1-0.000^82] 

In  order  that  Wa  may  be  infinitely  great,  the  divisor  of  the  second  term  must 
be  equal  to  zero,  or 


ECONOMICS   OF   STEEL   ARCH-BRIDGES 


241 


This  is  the  theoretical  Hmiting  span-length  for  three-hinged  arches  of 
carbon  steel,  or  the  span  at  which  such  an  arch  could  carry  nothing  but 
its  own  weight  without  being  over-stressed.  It  will  be  noted  that  this 
limiting  length  is  the  reciprocal  of  the  dead-load  coefficient  in  Equation  (4), 
and  that  a  vertical  line  on  the  diagram  of  arch-rib  weights  per  lineal  foot  of 
span,  drawn  through  the  abscissa  point  which  represents  this  value  of  Z, 
will  be  asymptotic  to  the  weight  curve. 

Fifth.  From  the  curves  in  the  diagrams  it  is  possible  to  determine  the 
economic  or  practicable  limit  of  arch  spans,  by  assuming,  as  the  author 
did  years  ago  in  his  economic  investigations  for  cantilevers,  that  the  said 


80000 


9000O 


70  00O 


30  000' 


10  000> 


1100         1300         1500         1700         1900         2100        2300        2600 
Span,  in  Feet. 


Fig.  26e.     Weights    of    Metal    in    Double-Track,    Steam-Railway,    Long-Span   Arch- 
Bridges  of  Carbon  Steel  for  Class-60  Live-Load. 


limit  is  reached  when  it  takes  4|  lbs.  of  metal  to  carry  1  lb.  of  live  load.  On 
that  basis,  and  assuming  that  the  equivalent  uniform  live  load  per  lineal  foot 
for  a  long  span  is  equal  to  the  car  load  per  lineal  foot,  the  limiting  weight  of 
metal  per  foot  for  carbon-steel,  double-track,  steam-railway  bridges  of 
Class  60  would  be  4.5X12,000  =  54,000  lbs.  Referring  to  Fig.  26e,  it  is 
found  that  the  span  for  that  weight  is  nearly  2,100  ft.;  consequently,  gen- 
erally speaking,  it  may  be  stated  that,  for  steam-railway  arch-bridges  of 
carbon  steel,  the  limiting  length  of  span  is  about  2,000  ft.,  or  the  same  as  the 
limiting  length  of  main  opening  in  cantilever  bridges  built  of  the  same 
material.  Judging  by  analogy,  the  corresponding  practicable  limiting 
length  of  nickel-steel  arch-spans  is  about  2,600  ft. 

Sixth.     It  is  impracticable  to  take  the  substructure  into  account  when 


242 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XXVI 


making  general  economic  investigations  for  arch  bridges,  because  no  two 
examples  thereof  are  alike.  In  case  of  a  succession  of  long  spans  in  which 
there  is  a  choice  of  rise,  a  tentative  layout  should  be  made  using  the  antici- 
pated economic  ratio  of  rise  to  span-length  when  both  substructure  and 
superstructure  costs  are  considered,  then  the  costs  of  piers  and  spans  should 


1.13^ 


0.15  0.20  0.25  0.30  O.i 

Ratios  of  Rise  to  Span  Lengrth. 


0.60 


Fig.  26/.     Economics  of  Solid-Rib  Arches,  with  Columns  and  Bracing,  for  Steam- 
Railway  Structures,  in  Relation  to  Ratios  of  Rise  to  Span-Length. 

be  computed,  the  uneconomic  effect  of  departing  from  the  established 
economic  ratio  of  rise  to  span-length,  given  in  Figs.  26/  to  26f ,  inclusive, 
being  employed  to  calculate  the  weights  of  metal  from  those  shown  in 
certain  other  fliagrams. 

Next,  this  work  should  be  repeated  for  a  slightly  greater  ratio  of  rise 
to  span-l(>ngth,  and  then  for  a  slightly  smaller  ratio  thereof.  These  three 
sets  of  computations  would  probably  determine  the  best  ratio  to  adopt; 


ECONOMICS   OF   STEEL   ARCH-BRIDGES 


243 


but,  if  not,  still  another  set  of  calculations  would  be  necessary.  The  com- 
putation work  involved  in  this  investigation  is  not  as  great  as  a  perusal  of 
the  preceding  directions  might  lead  one  to  surmise,  especially  after  the 
computer  has  become  accustomed  to  utilizing  the  diagrams  of  the  paper  and 
to  estimating  quickly  the  approximate  quantities  of  masonry  in  arch  piers. 


O.Oi) 


0,15  0.20  0.25  0.30  0.35 

Ratios  of  Rise  to  Span  Length. 


0.45 


1.13 


l.OS 


1.02 


0.60 


Fig.  26g.     Economics  of  Solid-Rib  Arches  for  Steam-Railway  Structures  (Ribs  Alone 
Considered),  in  Relation  to  Ratios  of  Rise  to  Span-Length. 


Seventh.  In  the  cantilever  arch  the  reduction  of  the  horizontal  thrusts 
at  the  tops  of  the  piers,  as  compared  with  simple  or  non-cantilevered  arches, 
effects  a  decided  saving  in  the  cost  of  the  said  piers;  and  the  greater  the 
proportionate  lengths  of  the  flanking  spans  to  the  arch  span,  the  larger  the 
economy  in  pier  material. 

Eighth.  Some  engineers  who  adhere  to  old-fashioned  notions  contend 
that  both  masonry  and  steel  arch-bridges  are  applicable  to  bed-rock  foun- 


244 


ECONOMICS    OF   BRIDGEWORK 


Chapter  XXVI 


dations  only,  and  that  the  piers  and  abutments  therefor  should  never  rest 
on  piles.  While  it  is  true  that  bed-rock  is  the  ideal  foundation  for  such 
structures,  pile  foundations  can  be  made  entirely  satisfactory,  provided  that 
the  masonry  of  the  bases  is  carried  well  down  into  firm  material  which  is 
capable  of  resisting  properly  the  horizontal  thrusts.  It  is  not  legitimate  to 
count  upon  the  horizontal  resistance  of  the  piles;  and  it  would  be  criminal 
practice  to  rest  the  piers  and  abutments  of  an  arch  bridge  on  piles  the  tops 
of  which  below  the  pier  bases  act  like  stilts  because  of  passing  through  soft 
material  before  reaching  a  hard  bearing. 


0.05 


0.15  0.20  0.25  0.30  0.35 

Ratios  of  Rise  to  Span  Length 


Fig.  26/i.     Economics  of  Braced-Rib  Arches,  with  Columns  and  Bracing,  for  Steam- 
Railway  Structures,  in  Relation  to  Ratios  of  Rise  to  Span-Length. 


Ninth.  As  stated  by  Mr.  F.  H.  Frankland  in  his  discussion,  "in  respect 
to  arch  designing,  the  proper  determination  of  the  true  economics  calls  for 
more  judgment  on  the  part  of  the  designing  engineer  than  with  any  other 
type  of  bridge." 

The  paper  and  the  resume  combined  contain  twenty-six  diagrams,  of 
which  only  ten  have  been  reproduccnl  in  this  cliapter;  hence  the  reader 
who  desires  to  utilize  the  I'esults  of  that  inv(>stigation,  is  referred  to  the 
paper  itself,  which,  with  all  the  discussions  and  the  resume,  is  soon  to  be 
pubhshed  in  the  "Transactions"  of  the  American  Society  of  Civil  Engi- 
neers. 

As  previously  indicated,  the  comparative  economics  of  steel  arch-bridges 


ECONOMICS   OF   STEEL   ARCH-BRIDGES 


245 


and  the  corresponding  bridges  of  simple-truss  or  cantilever  type  depend 
greatly  upon  the  governing  conditions  for  the  substructure,  and  that,  as 
these  almost  invariably  differ  essentially  at  proposed  crossings,  it  is  imprac- 
ticable to  determine  in  general  the  economics  of  substructure  for  such  com- 


0.15  0,20  0.25  0,30 

Ratios  of  Rise  to  Span  Length. 


Fig.  26i. 


Economics  of  Braced-Rib  Arches  for  Steam-Railway  Structures  (Ribs  Alone 
Considered),  in  Relation  to  Ratios  of  Rise  to  Span-Length. 


parisons,  each  case  having  to  be  treated  upon  its  own  merits.  While  this 
is  certainly  true,  it  is  practicable,  nevertheless,  to  outline  some  general 
principles  that  will  enable  a  bridge  designer  to  determine  readily  the  suit- 
ability of  any  proposed  crossing  for  an  arch  layout,  as  affected  by  sub- 
structure conditions;  and  the  author  offers  the  following: 


246 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XXVI 


First.     Where  there  is  a  gorge  with  steep,  rocky  sides  to  be  crossed  hy  a 
single  span,  the  arch  is  eminently  suitable;  for  not  only  does  it  reduce  the 


Fig.  2Q/.     Canadian  Northern  Pacific  Railway  Bridge  over  the  Fraser  River  at 

Lytton,  B.  C 


Fif!.  2U:.     Arch  Bridge  over  llic  ^^';lik,■ll()  IJivor  at  Hamilton,  N.  Z. 


required  volume  of  masonry  to  a  minimum  but  also  it  bi'ings  the  pressure 
on  the  rock  foundations  practically  normal  to  the  surface — a  coiisi(l(>jatioii 


ECONOMICS   OF   STEEL   ARCH-BRIDGES  247 

often  of  great  importance  when  the  rock  would  be  subject  to  shp  under 
vertical  loading.  A  good  illustration  of  such  a  condition  is  the  author's 
Fraser  River  Bridge  at  Lytton,  British  Columbia,  shown  in  Fig.  2Qj. 

Second.  Where  there  is  a  navigable  stream  to  be  crossed  by  a  single 
span,  and  where  the  material  near  the  water's  edge  is  either  rock  or  some 
fairly-hard  material,  such  as  shale  or  stiff  clay,  a  deck  truss-bridge  would  be 
inadmissible  on  account  of  navigation,  and  a  through  truss-bridge  would 
involve  high,  expensive  piers;  hence,  under  these  circumstances,  an  arch 
structure  would  be  economic.  Two  of  the  author's  bridges  over  the 
Waikato  River  in  New  Zealand,  shown  in  Figs.  26A;  and  2QI,  illustrate  such 
conditions. 


h 


L 


Fig.  2GL     Arch  Bridge  over  the  Waikato  River  at  Cambridge,  N.  Z. 

Third.  Where  the  foundations  of  a  wide  crossing  are  either  solid  rock  or 
some  other  hard  material  lying  close  to  the  bed  of  the  stream  or  to  the  sur- 
face of  the  banks  thereof,  and  where  the  grade  line  is  much  above  the  high- 
water  line,  a  layout  consisting  of  a  succession  of  arch  spans  will  frequently 
be  economic.  The  springings  of  the  arches  can  be  brought  down  close  to 
the  high-water  line  or  to  the  ground,  as  the  case  may  be,  giving  small 
piers ;  whereas,  for  a  deck  simple-truss  layout,  much  higher  piers  would  be 
required.  An  excellent  illustration  of  such  conditions  is  given  by  the 
author's  highway  bridge  over  the  Arroyo  Seco  at  Pasadena,  Calif.,  shown  in 
Fig.  26w. 


248 


ECONOMICS    OF    BRIDGEWORK 


Chapter  XXVI 


e3 
O 


Another  illustration  of  the  said  conditions,  in  which  the  economic  advan- 
tage of  the  arch  is  not  so  marked, 
is  the  author's  combined-high- 
waj^-and-electric-railway  bridge 
over  the  Colorado  River  at 
Austin,  Texas,  shown  in  Fig.  26n. 
Here  the  vertical  distance  from 
high-water  to  pier-base  is  con- 
siderable, thus  rendering  the  piers 
much  more  expensive  than  those 
of  the  Pasadena  structure. 

Where  the  foundation-level 
is  much  below  the  river-bed, 
the  conditions  are  not  favorable 
to  the  arch;  because,  in  order 
properly  to  resist  the  horizontal 
thrust,  the  piers  have  to  be 
made  much  wider  ^than  those 
for  simple-truss  spans. 

Before  concluding,  it  might 
be  well  to  quote  the  following 
caution  given  by  the  author  to 
those  intending  to  utilize  the 
information  furnished  in  his 
memoir : 

The  various  formulse  and  dia- 
grams in  this  paper  are  to  be  con- 
sidered as  merely  approximate;  and 
though  they  are  sufficiently  accurate 
for  preliminary  estimates  and  for  ob- 
taining trial  dead  loads,  they  should 
not  be  used  by  contractors  in  tender- 
ing on  work.  The  reason  for  this 
uncertainty  is  that  the  varying  physi- 
cal conditions  at  different  crossings 
affect  the  arch  layouts  to  such  an 
extent  as  materially  to  influence  the 
weight  of  metal  required.  As  the 
formulae  were  based  on  economic 
functions,  the  weights  given  by  their 
use  might  very  properly  be  considered 
as  the  minima  possible;  and  any  un- 
economic conditions  which  may  exist 
will  involve  an  increase  thereof,  the 
ainontit  being  a  matter  to  be  deter- 
iniiicd  by  the  computer's  judgment. 


ECONOMICS    OF    STEEL   ARCH-BRIDGES 


249 


CHAPTER  XXVII 

ECONOMICS     OF     STEEL    TRESTLES,     VIADUCTS,     AXD     ELEVATED    RAILROADS 

The  usual  railway  steel  trestle  consists  of  alternate  towers  and  inter- 
mediate spans.  In  determining  the  economic  span-lengths  for  such  a 
structure,  there  are  two  separate  factors  to  be  studied : 

1.  The  ratio  of  length  of  intermediate  span  to  that  of  tower-span. 

2.  The  cUstance  from  center  to  center  of  towers. 

Investigation  of  the  fu'st  of  these  factors  for  a  single-track-railwaj' 
trestle  shows  that,  for  Class  40  loacUng,  the  length  of  tower-span  should  vary 
from  44  per  cent  of  the  distance  between  centers  of  towers  for  a  trestle  60 
feet  high,  to  35  per  cent  thereof  for  one  240  feet  high,  the  length  of  inter- 
mediate span  for  these  limits  being  from  1.27  to  1.86  times  that  of  the  tower- 
span.  For  a  Class  70  loading  the  corresponding  percentages  for  tower-spans 
vary  from  46  to  38,  and  the  corresponding  span-ratios  from  1.18  to  1.63. 
After  the  fii-st  factor  has  been  investigated  the  second  one  can  be  deter- 
mined. 

Fig.  27a  gives  the  economic  distances  from  center  to  center  of  towers 
and  the  economic  lengths  of  intermediate  and  tower-spans  for  single-track 
railway  trestles,  varying  in  height  from  60  feet  to  240  feet,  and  for  Classes 
40  to  70.  Considerable  variation  from  these  economic  relations  will  affect 
the  total  weights  but  slightly.  It  will  be  noted  that  the  economic  lengths 
are  considerably  greater  for  Hght  loadings  than  for  hea\'A'  ones. 

Fig.  55oo  on  page  1259  of  "Bridge  Engineering"  covers  the  same  data 
as  Fig.  27a,  but  the  lengths  there  given  are  incorrect.  In  the  investigation 
for  Fig.  55oo  no  attempt  was  made  to  ascertain  the  economic  ratio  of 
intermediate  span-length  to  tower  span-lengih,  it  being  assumed  that  it 
would  be  sufficiently  accurate,  in  determining  the  economic  distance  from 
center  to  center  of  towers,  to  consider  the  length  of  the  tower-span  fixed, 
and  to  vary  the  length  of  the  intermediate  span  only. 

The  weights  of  longitudinal  bracing  given  in  Fig.  oopp  on  page  1260  of 
"Bridge  Engineering"  are  also  incorrect.  The  weights  should  vary  from 
450  pounds  per  vertical  foot  for  30-foot  tower-spans  to  580  pounds  for  60- 
foot  tower-spans,  being  independent  of  the  height. 

The  total  weights  of  metal  given  by  Fig.  D5rr  on  page  1262  of  "Bridge 
Engineering"  are  but  slightly  in  error,  being  about  2  per  cent  too  great  for 
a  60-foot  height,  and  about  6  per  cent  too  small  for  a  240-foot  height. 

In  Fig.  276  are  given  the  economic  span-lengths  for  various  heights  of 
low,  single-track-railway  trestles  consisting  of  towers  with  two  rocker 

250 


STEEL   TRESTLES,    VIADUCTS,    AND    ELEVATED    RAILROADS      251 


bents  between,  as  shown  in  a  corner  of  the  diagram.     It  will  be  noted  that, 
as  in  the  previous  type,  the  lighter  the  live  load  the  greater  the  economic 

60       60        100        120        140        160        ISO        200       220        240       260 


ao         100        IZO 
/fe/^hf  of  lower  m  feef. 


240       260 


Fig.  27a. 


140         160         JdO        ZOO       220 

Top  of  Masonry  fo  Base  of  2a}/. 

Economic  Span-Lengths  for  High,  Single-Track-Railway  Trestles. 


span-length.     It  has  been  assumed  that  the  length  of  tower-span  would  in 
all  cases  be  30  feet.     Actually,  this  length  should  vary  somewhat,  increas- 


252 


ECONOMICS    OF   BRIDGEWORK 


Chapter  XXVII 


ing  slightly  with  the  height;  but  the  resulting  error  in  the  total  weights  of 
metal  will  be  negligible. 

For  double-track-railway  trestles  consisting  of  alternate  tower-spans 
and  intermediate-spans,  and  having  two  planes  of  longitudinal  bracing, 
the  ratio  of  intermediate-spanrlength  to  tower-span-length  is  a  trifle  less 
than  for  the  single-track  trestle,  the  values  for  Class  40  being  about  1.08  for 
a  60-foot  height,  and  1.55  for  a  240-foot  height.  The  corresponding  values 
for  Class  70  are  1.05  and  1.34.  The  economic  distances  from  center  to 
center  of  towers  are  85  or  90  per  cent  of  those  for  a  single-track  trestle. 
The  lengths  of  tower-spans  are  about  the  same  as  for  the  single-track 
trestles,  but  the  lengths  of  intermediate-spans  are  only  about  80  per  cent 
as  great. 


10         iO 


70         60         90        100, 


1      90     m 

Fig.  276.     Economic  Span-Lengths  for  Low,  Single-Track-Railway  Trestles. 


■JO        iO         30         40         30         60         70 
Hei0  in  /ie/,  I>p  of  Mason  j  to  ^se  of  2a/f 


The  economics  for  low,  double-track-railway  trestles  of  the  type 
shown  in  Fig.  276  are  as  follows: 

The  lengths  of  the  tower-spans  will  be  identical  with  those  for  like 
single-track-railway  trestles,  and  those  of  the  intermediate  spans  about 
ninety  per  cent  of  the  corresponding  lengths  for  same. 

Strictly  speaking,  the  costs  of  the  pedestals  should  be  figured  in  comput- 
ing the  economic  span-lengths,  but  for  bare  rock  foundations  they  are 
insignificant  and,  therefore,  negligil)le;  for  pile  foundations  and  spread 
foundations  on  soft  soil  they  are  almost  constant  \)q\'  lineal  foot  of  stmcture, 
irrespective  of  the  span-lengths,  and  consequently  also  negligible;  and  it  is 
only  when  the  pedestals  have  to  penetrate  dee]:)l>'  into  the  ground  and  rest 
on  fairly  hard  soil  that  their  cost  boc^omes  influential.  TluMr  c^lTcct  is  to 
increase  the  economic  lengths  of  both  the  intern unliate  and  Ilu>  tower  spans, 
although  probably  not  more  than  a  few  feet. 

The  economic  span-knigths  for  highway  trestles  with  two  lines  of  main 
girders  will  generally  be  a  trifle  greater  than  those  for  Class  40,  single- 
track-railway  trestles;  and  for  like  structuix^s  with  several  lines  of  main 
girders  they  will  be  somewhat  larger  than  those  for  C^lass  40,  double-track- 


STEEL   TRESTLES,    VIADUCTS,    AND    ELEVATED   RAILROADS      253 

railway  trestles.     The  economic  lengths  will  be  greater  for  hght  live  loads 
and  timber  decks  than  for  heavy  live  loads  and  concrete  decks. 

The  economics  of  column  spacing  for  bents  when  cantilever  brackets  are 
employed  is  an  interesting  little  problem,  but  the  final  determination  must 
be  in  accordance  with  good  judgment  as  well  as  economy;  for  if  the  spacing 
be  too  small,  rigidity  is  Ukely  to  be  sacrificed.  Upon  certain  assumptions 
of  approximate  correctness  the  mathematical  solution  of  this  problem  is  a 
possibility;  but  the  equations  involved  would  be  so  complicated  that  it  is 
much  better  for  any  particular  case  to  assume  two  or  three  spacings,  com- 
pute the  total  weight  of  metal  in  the  bent  for  each,  and  find  the  one  which 
will  give  approxi^nately  the  least  weight  of  metal.  If  the  columns  are 
placed  at  the  quarter  points  of  the  beam,  the  dead-load  bending-moment 
at  the  middle  will  be  approximately  zero;  and  if  the  effect  of  stress  rever- 
sion is  ignored,  the  direct  and  the  reverse  bending  moments  for  the  central 
portion  of  the  beam  will  be  equal,  and  this  arrangement  would  be  about  the 
most  economical  possible.  But  if  reversion  is  considered,  the  sectional 
area  of  the  middle-portion  of  the  beam  must  be  greater  than  that  of  the 
outside  portions,  hence  for  economy  its  length  should  be  somewhat  less 
than  one-half  of  the  total,  and  the  columns  would  then  be  spaced  somewhat 
closer  than  when  they  are  located  at  the  quarter  points.  The  fact  that  the 
brackets  are  usually  lighter  near  the  outer  ends  than  at  the  inner  ones 
would,  for  economy,  tend  to  draw  the  columns  together;  but,  on  the  other 
hand,  this  would  increase  the  weight  of  the  splices  and  connecting  details. 
The  proper  column  spacing  to  adopt  will  depend  upon  the  length  of  the 
columns;  for  it  is  easily  conceivable  that  the  structure  could  be  so  high  and 
so  narrow  that  the  quarter-point  spacing  would  be  too  close  for  proper 
resistance  to  wind  pressure.  Again,  in  such  a  case  the  wind  load  might 
be  so  great  as  to  necessitate  an  increase  in  column  section  above  that 
required  to  care  for  the  live  and  dead  load  stresses  only;  and  thus  the  effect 
of  wind  pressure  would  enter  the  economic  study.  It  will  be  found  in  most 
cases  that  it  is  inadvisable  to  space  the  columns  much  less  than  one-half  of 
the  total  length  of  the  beam. 

Elevated  Railroads 

In  respect  to  the  economics  for  Elevated  Railroads,  as  long  ago  as  1896 
the  author,  when  designing  the  Northwestern  Elevated  and  the  Union 
Loop  Elevated  Railroads  of  Chicago,  determined  certain  economic  functions 
for  such  structures  and  published  the  results  in  a  paper  entitled  "A  Study 
in  Designing  and  Construction  of  Elevated  Railroads,  with  Special  Refer- 
ence to  the  Northwestern  Elevated  Railroad  and  the  Union  Loop  Elevated 
Railroad  of  Chicago,  III,"  which  paper  was  presented  to  the  American 
Society  of  Civil  Engineers  and  published  in  its  "Transactions"  for  1897. 
From  it  the  following  statements  concerning  the  economics  of  elevated- 
railroads  have  been  excerpted: 


254  ECONOMICS   OF   BEIDGEWORK  Chapter  XXVII 

Best  and  Most  Economical  Span-Lengths 

This  question  was  investigated  very  exhaustively,  considering  every 
item  of  expense,  including  not  only  the  cost  of  metal  in  place,  but  also  that 
of  concrete,  excavation,  back-filUng,  and  pavement;  also  the  possibihty  of 
expense  for  the  moving  of  water  pipes  and  other  conduits.  The  investiga- 
tion showed  that,  for  plate-girder  construction  through  private  property, 
the  econoinic  span-length  is  about  40  ft.  for  intermediate  spans  and  23  ft. 
for  tower  spans;  while  for  construction  in  the  street,  where  towers  are  inad- 
missible, it  varies  from  47  to  50  ft.,  or  even  3  or  4  ft.  more,  in  case  of  cross- 
girders  spanning  wide  streets  from  curb  to  curb. 

The  theory  of  true  economy  in  elevated  railroad  designing,  as  far  as 
length  of  bays  is  concerned,  is  simply  this:  "The  cost  of  the  longitudinal 
girders  should  be,  as  nearly  as  may  be,  equal  to  the  cost  of  the  bents  and 
their  supporting  pedestals,  in  cases  of  doubt  adopting  the  longer  span." 

Four-Column  versus  Two-Column  Structures 

Detailed  estimates  of  cost  show  that,  as  far  as  economy  is  concerned, 
there  is  but  little,  if  any,  difference  between  these  two  styles  of  bent. 
Whether  the  total  cost  of  the  four-column  bent  will  exceed  that  of  the  two- 
column  one  for  a  four-track  structure  depends  upon  the  various  schedule 
prices  for  metal,  concrete,  excavation,  paving,  etc.,  as  well  as  upon  the 
character  of  the  soil.  As  there  is  no  great  difference  in  the  cost  of  these 
two  types  of  structure,  and  as  the  four-column  bent  is  decidedly  the  more 
rigid  of  the  two,  it  was  adopted  wherever  practicable.  Cantilevering  an 
entire  train  load  beyond  the  exterior  column  of  a  two-column  bent  is  not 
conducive  to  rigidity,  but  this  is  the  only  method  that  will  bring  the  cost 
as  low  as  that  of  the  four-column  bent. 

Braced  Towers  versus  Solitary  Columns 

Where  an  elevated  railroad  occupies  private  property  and  crosses 
the  streets  by  spanning  from  curb  to  curb,  it  is  practicable  to  use  braced 
towers  and  thus  stiffen  the  structure  and  check  vibration;  and,  moreover, 
this  arrangement  is  very  economical. 

For  the  Northwestern  Elevated,  upon  which  it  is  proposed  to  rim 
trains  at  a  speed  of  40  miles  per  hour  on  the  inner  tracks  between  the 
inter-track  stations,  situated  about  a  mile  apart,  the  consideration  of  the 
extra  rigidity  afforded  by  the  braced  towers  is  quite  important.  It  was 
therefore,  decided  to  use  both  longitudinal  and  transverse  sway  bracing, 
forming  braced  towers  spaced  about  150  ft.  apart  (or  two  towers  per  block), 
and  to  use  the  transverse  sway  bracing  in  all  bents  on  curves,  wherever 
practicable. 

Two  only  of  the  three  spaces  between  columns  have  transvci'se  sway 


STEEL    TRESTLES,    VIADUCTS,    AND    ELEVATED    RAILROADS      255 

bracing,  thus  leaving  a  longitudinal  passageway  for  wagons  at  the  center 
of  the  structure. 

The  saving  in  weight  of  metal  per  lineal  foot  of  four-track  structure  on 
tangents  by  adopting  braced  towers  instead  of  solitary  columns  was 
found  to  be  about  140  lbs.,  or  nearly  9  per  cent  of  the  total  weight. 

Plate  Girders  versus  Open-Webbed  Girders 

In  designing  these  elevated  railroads  for  Chicago,  many  estimates  were 
made  for  both  plate-girders  and  open-webbed  girders,  which  demonstrate 
that  there  is  practically  no  difference  in  the  weight  when  both  girders  are 
properly  designed.  As  the  open-webbed  girders  cost  a  trifle  more  per 
pound  to  manufacture,  there  is  no  economy  in  their  use;  nevertheless 
they  were  adopted  for  all  structures  running  longitudinally  in  the  streets, 
in  order  to  comply  with  certain  city  ordinances.  The  observance  of  these 
ordinances  was  sometimes  carried  to  extremes,  producing  ridiculous  com- 
binations of  solid  and  open  web  in  the  same  girder,  and  an  evident  waste 
of  material  and  labor.  For  this  the  engineers  are  not  to  blame,  because 
they  did  not  frame  the  ordinances. 

Best  Sections  for  Columns 

Investigations  concerning  strength,  capacity  to  resist  impact,  facility 
of  erection,  economy  of  metal,  etc.,  determined  that  the  section  for  columns 
located  in  the  street  should  be  two  15-in.  rolled  channels  with  the  flanges 
turned  inward  and  a  15-in.  rolled  I-beam  riveted  between  to  act  as  a  cen- 
tral web  or  diaphragm,  the  flanges  of  the  channels  being  held  in  place  by 
interior  stay  plates  spaced  about  3-feet  centers.  In  most  cases  the  column 
feet  pass  below  the  pavement  and  are  embedded  in  the  concrete,  to  which, 
of  course,  they  are  bolted,  but  in  some  cases  they  rest  on  pedestals  a  little 
above  the  level  of  the  sidewalk.  The  main  object  in  turning  the  flanges 
inward  is  to  enable  the  column  better  to  resist  impact  from  heavily  loaded 
vehicles.  Just  above  the  pavement  there  is  a  curved  casting  filled  with 
concrete  and  surrounding  the  column  to  act  as  a  fender. 

This  type  of  column  is  very  satisfactory  after  it  is  erected,  although 
it  gives  some  little  difficulty  in  the  shops  and  involves  slightly  more  field 
riveting  than  usual.  One  complaint  made  was  that  the  planes  of  the 
top  and  bottom  flanges  of  I-beams  are  never  exactly  parallel  to  each  other, 
hence  some  straightening  was  necessitated. 

For  columns  located  on  private  property  or  on  sidewalks  where  the 
structure  is  transverse  to  the  street,  four  Z-bars  and  a  web  plate  were 
adopted  as  the  most  satisfactory  section.  At  the  top  of  the  column  a 
wide,  curved  web-plate  and  curved  angles  were  used.  This  design  makes 
a  most  satisfactory  column,  which  goes  through  the  shops  readil}^,  and 
which  is  well  adapted  for  quick  erection.     It  is  true  that  it  necessitated  a 


256  ECONOMICS   OF   BRIDGEWORK  Chapter  XXVII 

special  tool  for  cutting  the  webs  to  a  circular  curve,  but  after  this  was 
made,  the  manufacture  was  easy  and  comparatively  inexpensive. 

In  Engineering  News  of  May  20,  1915,  there  appeared  an  excellent 
article  by  Mr.  Maurice  E.  Griest,  Assistant  Designing  Engineer  of  the 
Public  Service  Commission  of  New  York  City,  entitled  "Design  of  Steel 
Elevated  Railways,  New  York  Rapid  Transit  System,"  in  which  he  gives  a 
diagram  showing  that  for  structures  located  in  the  street  the  economic 
span-length  is  fifty  feet,  but  that  for  lengths  from  forty-five  feet  to  fifty- 
five  feet  there  is  not  much  difference  in  the  cost.  This  not  only  confirms 
the  author's  findings  of  two  decades  earlier,  but  also  is  in  accordance  with 
a  general  deduction  made  by  him  of  late  from  several  economic  investi- 
gations, viz.,  that,  up  to  a  certain  limit,  a  material  variation  from  abso- 
lutely economic  conditions  can  generally  be  made  without  seriously 
increasing  the  total  cost,  but  when  the  said  limit  is  passed  the  uneconomics 
involved  increases  rapidly. 

For  further  information  concerning  the  details  of  elevated  railroads, 
the  reader  is  referred  to  the  before-mentioned  "Transactions"  of  the 
American  Society  of  Civil  Engineers. 


CHAPTER  XXVIII 


ECONOMICS    OF    CANTILEVER    BRIDGES 


Cantilever  bridges  inay  be  divided  into  four  types,  which  cover 
all  the  layouts  that  are  used  by  good  designers.  These  are  shown  as 
Types  A,  B,  C,  and  D,  in  Fig.  12a. 

Type  A  is  the  one  ordinarily  adopted — probably  as  often  as  three 
times  out  of  four.  It  is  applicable  to  the  case  of  a  fairly-wide  crossing, 
where,  for  some  reason  or  other,  it  is  not  permissible  or  advisable  to  put 
piers  in  the  deep  water. 

Type  B  really  amounts  to  the  doubling  up  of  two  Type-A  structures  by 
omitting  the  anchorages  at  the  junction  and  forming  the  anchor  arms 
into  one  continuous  span.     It  is  applicable  to  very  wide  rivers. 

Type  C,  which' is  the  most  economic  of  the  four,  is  used  occasionally 
instead  of  three  simple-truss  spans,  either  for  reasons  connected  with  the 
navigation  of  the  stream  or  because  of  economic  motives  that  are  some- 
times based  on  reahty  but  too  often  upon  unwarranted  assumption.  This 
question  is  discussed  at  length  in  Chapter  XII . 

Type  D  is  a  combination  of  Types  B  and  C,  as  can  be  seen  by  an  inspec- 
tion of  the  layout  in  Fig.  12a. 

Comparing  Types  A  and  B,  a  glance  at  the  two  layouts  of  the  diagram 
shows  that  there  can  be  but  little  difference  in  the  weights  of  metal  per  lineal 
foot  of  entire  bridge;  because,  while  the  weight  per  foot  for  the  anchor 
span  is  generally  somewhat  greater  than  that  of  the  anchor  arms,  the 
entire  weight  of  two  anchorages  is  saved,  whatever  net  difference  there  is 
constituting  generally  an  excess  for  Type  B.  There  can,  however,  be  no 
real  comparison  between  these  two  types  for  any  particular  case,  as  one  is 
for  a  comparatively  narrow  crossing  and  the  other  for  a  very  wide  one. 

Comparing  Types  A  and  C  for  a  crossing  in  which  the  over-all  length 
is  fixed,  but  where  the  intermediate  piers  can  be  placed  as  desired,  the 
ratio  of  the  weight  of  Type  C  to  that  of  Type  A  varies  from  about  0.8  for 
structures  under  two  thousand  feet  in  length  to  about  0.65  for  structures 
three  thousand  feet  long.  The  method  of  determining  this  may  best  be 
illustrated  by  an  example. 

Given  Class  70  live  load  and  a  total  length  of  structure  of  2500',  we 
have  from  Fig.  12a  for  Type  A. 

3^L+i|L+3^L  =  f|L  =  2500'.-.  L=1538' 
and  for  Type  C, 

H^+if  ^+liL  =  f|L  =  2500'.-.  L=1250'. 

257 


258  ECONOMICS   OF  BRIDGEWORK  Chapter  XXVIII 

From  Fig.  55ddd  on  page  1274  of  "Bridge  Engineering"  we  find,  for 
Class  70  and  L  =  1538',  a  weight  of  metal  per  foot  of  28,000  lbs. ;  and  from 
Fig.  55jjj  on  page  1282  thereof,  for  that  loading  and  L  =  1,250',  a  weight  of 
21,000  lbs.     The  ratio  of  these  weights  is  fi  =  0.75. 

Comparing  Type  D  with  the  other  types  in  Fig.  12a,  it  is  evident 
that,  for  the  same  value  of  the  hypothetical  opening,  L,  its  weight  of 
metal  is  intermediate  in  amount;  but,  as  before,  there  is  really  no  necessity 
for  contrasting  this  type  with  the  others,  because,  for  any  crossing  where 
it  would  be  suitable,  the  other  types  would  be  whoUy  unsuitable. 

Recapitulating,  there  is  never  any  necessity  for  a  discussion  as  to  which 
of  the  four  types  should  be  adopted  for  any  proposed  crossing,  because  the 
profile  thereof  with  its  governing  conditions  will  indicate  clearly  which  is 
the  only  type  appHcable;  but  there  is  occasionally  an  economic  question 
to  determine  as  to  whether  a  simple-truss  layout  or  a  cantilever  layout 
should  be  adopted.     This  question  is  treated  at  length  in  Chapter  XII. 

In  respect  to  the  economic  division  of  span-lengths  for  any  proposed 
layout,  the  author  determined  this  question  for  Type  A  nearly  a  quarter 
of  a  century  ago  when  writing  ''DePontibus,"his  findings  being  as  follows: 

First.  The  economic  length  of  the  suspended  span  is  about  three- 
eighths  (I)  of  the  length  of  the  main  opening,  but  a  considerable  increase 
or  decrease  of  this  proportion  does  not  greatly  change  the  total  weight  of 
metal. 

Second.  The  most  economic  length  of  anchor  arms,  where  the  total 
length  between  centers  of  anchorages  is  given,  and  when  the  main  piers 
can  be  placed  wherever  desired,  is  one-fifth  (|)  of  the  said  total  length,  or 
one-third  (|)  of  the  m^ain  opening.  By  keeping  the  anchor  arms  short, 
the  top  chords  may  be  built  of  eye-bars,  provided  that,  with  the  usual 
allowance  for  impact,  there  is  no  reversion  of  chord  stress ;  and  this  effects 
quite  an  economy  of  metal.  But  it  is  conceivable  that  cases  might  arise 
where,  from  danger  of  washout  of  falsework,  eye-bar  top  chords  would 
be  objectionable;  hence  this  method  of  economizing  must  be  used  with 
caution. 

It  must  not  be  forgotten  that  for  every  dollar  saved  by  reducing  the 
total  weight  of  metal  through  the  shortening  of  the  anchor  arm,  it  will  be 
necessary  to  spend  about  twenty  cents  for  extra  concrete  in  the  anchorages. 
On  that  account,  for  the  conditions  assumed,  the  truly  economic  length  of 
each  anchor  arm  of  a  three-span.  Type  A,  cantilever  bridge  may  be  a 
trifle  greater  than  twenty  per  cent  of  the  total  distance  between  centers  of 
anchorages. 

Dr.  Steinman  in  his  "Suspension  Bridges  and  Cantilevers,"  by  a 
theoretical  investigation  and  by  using  certain  constants  determined  from 
computed  structures,  shows  that  for  this  case  the  length  of  anchor  arm  for 
economy  should  be  four-tenths  of  the  main  opening,  or  four-eighteenths 
(0.22)  of  th(^  total  length  of  structure.  This  checks  quite  closely  with  the 
author's  long-previous  determination  of  "two-tenths  or  slightly  more." 


ECONOMICS    OF    CANTILEVER    BRIDGES  259 

Third.  When,  however,  the  problem  is  to  determine  the  economic 
length  of  anchor  arm  for  a  fixed  distance  between  main  piers,  the  result 
will  be  quite  different;  because,  within  reasonable  limits,  the  shorter  the 
anchor  arm  the  smaller  will  be  its  total  weight  of  metal,  and  because 
trestle  approach  is  much  less  expensive  than  anchor  arm.  It  would  not, 
for  evident  reasons,  be  advisable  to  make  the  length  of  anchor  arm  less 
than  twenty  per  cent  of  that  of  the  main  opening,  or  say  fifteen  per  cent 
of  the  total  distance  between  centers  of  anchorages.  With  this  length 
there  would  probably  be  no  reversion  of  stress  in  the  chords  of  the  anchor 
arm,  even  when  impact  is  considered.  Generally,  though,  the  appearance 
of  the  structure  would  be  improved  by  using  longer  anchor  arms  than  the 
inferior  Hmit  just  suggested. 

Fourth.  In  respect  to  the  economic  length  of  anchor-span  in  a  suc- 
cession of  cantilever  spans,  it  may  be  stated  that,  within  reasonable  limits, 
the  shorter  such  anchor-spans  are  the  greater  will  be  the  economy  involved ; 
but,  generally,  navigation  interests  wiU  prevent  their  being  built  as  short 
as  might  be  desired.  If  permissible,  they  may  be  made  so  short  that,  as 
in  the  case  of  anchor  arms,  eye-bars  may  be  used  for  the  top  chords,  thus 
effecting  a  decided  economy  of  metal,  although  shortening  the  anchor- 
span  increases  proportionately  the  stresses  on  the  web  members  and  the 
weights  thereof. 

In  regard  to  truss-depths  for  cantilever  bridges,  the  author's  practice 
is  to  make  that  for  the  suspended  span,  when  the  chords  are  parallel,  from 
one-fifth  of  its  length  for  short  spans  to  one-seventh  of  its  length  for  very 
long  ones,  interpolating  between  these  limits  for  intermediate  lengths. 
If  one  of  the  chords  be  polygonal,  a  greater  proportionate  truss  depth  at 
mid-span  and  a  smaller  one  at  the  ends  would  logically  be  employed. 
The  height  of  the  vertical  posts  over  the  main  piers  can  be  made  about 
fifteen  (15)  per  cent  of  the  length  of  the  main  opening,  or  not  to  exceed 
three  and  a  half  (3.5)  times  the  perpendicular  distance  between  central 
planes  of  trusses  over  the  main  piers.  In  the  new  design  for  the  Quebec 
bridge  these  posts  were  made  310  feet  high  for  the  sake  of  appearance, 
although  the  economic  length  was  found  to  be  only  290  feet.  These  figures 
correspond  to  percentages  of  main  openings  of  about  seventeen  (17)  and 
sixteen  (16)  respectively. 

There  are  certain  legitimate  economies  that  may  be  employed  in  the 
designing  of  cantilever  bridges,  among  which  may  be  mentioned  the  fol- 
lowing: 

A.  The  wind  pressure  assumed  in  computing  the  erection  stresses 
may  be  taken  lower  than  that  given  in  the  specifications  for  the  finished 
structure,  provided  that  the  full  wind  pressure  would  not  overstress  any 
of  the  metal  seriously  or  involve  any  risk  of  disaster  during  erection.  A 
stress  of  three-quarters  of  the  elastic  limit  of  the  metal  applied  a  few  times 
during  erection  would  do  no  harm;  and  the  chance  of  there  being  in  such 
limited  time  any  wind  pressure  at  all  approaching  in  magnitude  that 


260  ECONOMICS   OF   BRIDGEWORK  Cil4lPTEr  XXVIII 

specified  is  very  small.  This  lowering  of  the  intensity  of  wind  pressure 
may  be  the  means  of  avoiding,  in  a  perfectly  legitimate  manner,  the 
increasing  of  the  sections  of  a  nmnber  of  truss  members  because  of  erection 
stresses;  but  such  economizing  should  be  done  with  caution  after  a  thor- 
ough consideration  of  its  greatest  poss-ible  effects. 

B.  A  certain  amount  of  metal  can  sometimes  be  saved  by  splaying  the 
trusses  between  the  main  piers  and  the  ends  of  the  cantilever  and  anchor 
arms ;  but  unless  the  amount  thereof  be  fairly  large,  the  extra  pound  price 
of  the  metalwork  in  the  cantilever  and  anchor  arms  due  to  the  said  splay- 
ing may  more  than  offset  the  value  of  the  reduction. 

C.  A  small  economy  may  sometimes  be  accompHshed  by  omitting  dur- 
ing erection  from  the  cantilevered  portion  of  the  structure  all  parts  that 
are  not  essential  to  its  strength  before  the  coupHng  of  the  cantilevered  ends 
is  effected,  thus  reducing  the  erection  stresses  a  httle. 

D.  Solitary  piers  or  large  pedestals  under  the  main  vertical  posts  are 
sometimes  just  as  satisfactory  in  every  way  as  long,  continuous  shafts, 
especially  if  a  connecting  wall  of  reinforced  concrete  between  them  be 
employed.  Generally  they  will  be  found  to  involve  a  large  saving  in  the 
cost  of  the  substructure. 

E.  In  very  wide  cantilever  bridges  it  might  sometunes  be  advisable  to 
adopt  intermediate  trusses  so  as  to  economize  materially  in  the  weight  of 
the  floor-beams  and  sometimes  a  trifle  in  that  of  the  trusses,  also  because  of 
the  consequent  reduction  in  dead  load,  but  mainly  so  as  to  keep  within  rea- 
sonable limits  the  sizes  and  weights  of  the  pieces  to  be  handled  and  thus 
decrease  the  size  of  the  traveler  and  the  cost  of  the  erecting  machinery. 
On  the  other  hand,  though,  increasing  the  number  of  trusses  is  likely  to 
augment  a  little  the  percentage  of  weight  of  truss  details;  but,  where  the 
sections  of  members  are  large,  this  increase  would  be  small.  In  case  the 
wind  stresses  are  an  important  factor  in  the  proportioning  of  the  truss 
members,  the  employment  of  an  interior  truss  or  interior  trusses  might, 
by  the  reduction  in  areas  of  chord  sections,  cause  such  relatively-large 
wind-stresses  on  the  chords  of  the  exterior  trusses  that  the  additional  metal 
required  to  take  care  of  them  would  offset  all  the  saving  obtained  in  the 
ways  just  mentioned. 

F.  In  long-span  cantilever  bridges  the  stresses  on  the  truss  members 
that  rest  upon  the  piers  should  be  divided  among  as  many  such  members 
as  possible  by  using  an  inclined  strut  on  each  side  as  well  as  a  vertical  post, 
instead  of  carrying  all  the  loads  to  the  top  of  the  latter  by  tension  members, 
as  was  done  in  the  original  design  of  the  ill-fated  Quebec  bridge.  Again,  if 
a  lowering  of  the  inner  ends  of  the  cantilever  arms  be  permissible,  the  inclin- 
ing of  the  end  sections  of  the  bottom  chords  to  the  horizontal  will  take  up  a 
portion  of  the  load  that  is  carried  to  the  pier,  and  thus  will  rcnhu'e  the 
stresses  on  the  vertical  and  inclined  posts  assembling  there.  This  last 
feature  reduces  also  the  total  cost  of  the  masoniy  l)y  diminishing  the  height 


ECONOMICS    OF    CANTILEVER    BRIDGES  261 

of  the  main  piers,  and  saves  placing  the  tops  of  the  trusses  at  an  abnormal 
height  above  the  water. 

G.  If  there  be  any  choice  between  the  riveted  and  the  pin-connected 
types  of  construction  for  any  cantilever  bridge,  it  is  generally  better  to 
adopt  the  latter;  because,  as  cantilever  bridges  are  usually  employed  for 
long  spans  only,  pin-connected  work  is  the  more  suitable.  Again,  it  is  a 
little  lighter  than  riveted  work;  and,  therefore,  the  dead  load  on  the  struc- 
ture would  be  somewhat  less.  On  the  other  hand,  the  riveted  construc- 
tion is  so  much  more  rigid  than  the  pin-connected  that  it  is  preferable  to 
adopt  it  whenever  the  conditions  permit;  besides,  in  the  riveted  work  it  is 
not  necessary  to  stiffen  any  truss  members  for  erection,  although  it  might 
be  obligatory  to  increase  a  few  of  their  sectional  areas. 

H.  Very  large  compression  members  should  be  made  of  box  section 
so  as  to  do  away  with  latticing.  This  not  only  effects  an  improvement 
in  the  design,  but  also  saves  some  metal,  although  the  details  required 
afc  the  panel  points  to  distribute  the  stresses  from  the  cut  cover-plates  tend 
to  offset  the  saving  in  weight  of  lattice  bars  and  stay  plates. 

Professors  Merriman  and  Jacoby  present  in  their  ''Roofs  and  Bridges," 
Part  IV,  an  excellent  treatment  of  the  subject  of  cantilever  bridges,  dis- 
cussed mainly  from  the  theoretical  point  of  view.  Their  economic  investi- 
gations, which  are  based  upon  chord  weights  only,  show  that  for  a  three- 
span  cantilever  of  Type  A,  each  anchor  arm  should  be  about  twenty-one 
and  two-tenths  (21.2)  per  cent  of  the  total  length  of  structure.  This  is 
quite  a  close  agreement  with  the  twenty  (20)  per  cent  minimum  found  by 
the  more  accurate  and  practical  investigation  that  was  made  for  "De  Ponti- 
bus."  The  professors  find,  though,  thirty-nine  and  four-tenths  (39.4)  per 
cent  of  the  total  length  of  structure  for  the  economic  length  of  the  suspended 
span,  corresponding  to  about  sixty-eight  per  cent  of  that  of  the  main  open- 
ing, while  the  "De  Pontibus"  investigation  made  it  only  thirty-seven  and  a 
half  (37.5)  per  cent  thereof.  Actual  experience  has  repeatedly  shown  that 
the  economic  length  of  the  suspended  span  is  from  three-eighths  (|)  to  one- 
half  (^)  of  the  main  opening,  hence  the  professors'  figures  for  this  portion  of 
their  work  have  the  appearance  of  being  incorrect;  but  Prof.  Merriman 
has  explained  to  the  author  by  letter  that  he  assumed  the  truss  depth  to  be 
the  same  throughout  the  entire  structure.  This  assumption,  combined 
with  that  of  ignoring  the  effect  of  the  weight  of  the  web,  will  account  for 
the  large  d.^screpancy;  because  the  professors'  mathematics  have  been 
checked  and  found  to  be  faultless.  As  a  matter  of  fact,  though,  no  Ameri- 
can engineer  would  think  for  an  instant  of  making  the  truss  depth  constant 
throughout  the  structure,  because  for  economic  reasons  it  should  gen- 
erally be  about  twice  as  great  over  the  main  piers  as  in  the  suspended  span. 
European  engineers,  however,  often  fail  to  make  the  truss  depths,  espe- 
cially in  the  cantilever  and  anchor  arms,  great  enough  for  economy.. 


262  ECONOMICS   OF   BRIDGEWORK  Chapter  XXVIII 

The  professors  make  also  from  their  economic  investigations  the  fol- 
lowing deduction:  "The  cantilever  system  hence  has  no  theoretic  economy 
over  simple  trusses  when  the  piers  can  be  located  in  any  position;  moreover, 
when  the  influence  of  the  alternating  stresses  in  the  anchor  arm  and  the 
material  required  for  anchor  rods  are  taken  into  account,  it  is  at  a  marked 
disadvantage."  This  is  true  for  Type  A,  which  is  the  layout  employed  by 
the  professors;  but  it  is  not  correct  in  general. 

The  professors  are  right  in  their  surmise  that  "probably  the  common 
three-span-cantilever  bridge  has  a  lower  degree  of  economy  than  the 
arrangement  where  the  simple  trusses  are  in  the  end  spans,  as  in  the  Ken- 
tucky River  bridge";  for,  as  previously  stated,  Type-C  layout  requires 
only  from  eighty  to  sixty-five  per  cent  as  much  metal  as  does  that  of  Type 
A,  for  the  same  total  length  of  structure.  It  must  be  remembered,  how- 
ever, that,  as  previously  indicated,  the  comparison  is  hardly  fair  to  the 
common  three-span-cantilever,  because  the  latter  provides  a  greater  main 
opening  than  that  of  the  alternative  layout. 


CHAPTER  XXIX 


ECONOMICS    OF   SUSPENSION    BRIDGES 


In  the  designing  of  suspension  bridges  there  is  still  much  to  be  learned, 
because  so  few  of  them  have  been  built ;  and  this  is  as  it  should  be,  because 
they  are  not  an  economic  type  of  structure,  excepting  for  exceedingly  long 
spans,  or  in  the  case  of  a  very  -light  highway  bridge  at  the  crossing  of  a 
gorge  or  a  river  of  great  depth  and  swift  current  where  it  would  be  too 
expensive  to  build  piers  in  the  stream.  As  shown  in  Chapter  XIII,  for 
steam-railway  structures  suspension  bridges  are  more  expensive  than  can- 
tilever bridges  up  to  the  practicable  limiting  length  of  the  latter;  and, 
moreover,  in  respect  to  the  important  element  of  rigidity  the  former  are 
certainly  inferior.  But  the  suspension  bridge  has  its  legitimate  place  in 
engineering  construction,  and  that  is  for  long-span  highway  bridges  pure 
and  simple,  and  sometimes  when  they  carry  also  electric  railways.  There 
are  crossings,  hke  that  of  the  North  River  at  New  York  City,  where  the 
conditions  are  such  as  to  make  the  use  of  the  suspension  bridge  obligatory. 

It  is,  therefore,  well  worth  while  to  study  the  economics  of  the  type, 
even  to  the  extent  of  making  an  exceedingly  elaborate  investigation,  as  the 
author  did  lately  in  his  memoir  on  "Comparative  Economics  of  Wire 
Cables  and  High-Alloy-Steel  Eye-bar-Cables  for  Long-Span  Suspension 
Bridges,"  presented  in  May,  1920,  to  the  Engineers'  Society  of  Western 
Pennsylvania,  of  which  memoir  more  anon. 

In  designing  a  highway  suspension  bridge,  the  first  economic  point  to 
consider  is  that  of  the  deck  and  floor-system,  both  of  which  should  always 
be  made  as  light  as  the  ruling  conditions  wiU  allow,  because  the  heavier 
the  floor  the  £;reater  the  load  on  the  cables.  This  general  question  of 
economics  in  deck  and  floor-system  has  been  treated  in  Chapter  XXI,  to 
which  the  reader  is  referred.  While  it  is  certainly  advisable  to  cut  down 
the  dead  load  to  a  minimum,  it  would  be  anything  but  economic  to  adopt  a 
plank  base  for  the  pavement,  on  account  of  the  great  danger  from  fire 
which  that  type  of  construction  involves.  Modern  highway  bridges  call 
for  a  reinforced-concrete  base  for  pavement,  and  there  is  no  dodging  this 
issue;  but  in  suspension  bridges  it  should  be  made  as  hght  as  practicable 
by  using  closely-spaced  stringers  and  thus  reducing  the  thickness  of  slab 
to  a  minimum.  It  is  true  that  a  buckled-plate  floor  is  lighter  than  a  rein- 
forced-concrete  slab,  but,  until  quite  lately,  as  indicated  in  Chapter  XXI, 
experience  has  shown  it  to  be  so  lacking  in  rigidity  that  under  the  passage 

263 


264  ECONOMICS   OF   BETDGEWORK  Chapter  XXEX 

of  modern  wheel-loads  it  has  permitted  the  pavement  to  crack  and  eventu- 
ally to  break  up.  It  is  probable,  though,  that  Mr.  Byrne's  correction  of 
the  defect  will  permit  in  future,  with  perfect  safety,  the  emplojnnent  of 
tliis  type  of  flooring. 

When  the  electric  railway  tracks  are  entirely  separated  from  the  road- 
ways, it  is  economic  to  use  the  ordinary  open  floor  of  wooden  ties  with 
proper  guard-rails,  because  the  danger  from  fire  with  such  a  floor  is  not 
great;  and  even  if  some  of  the  ties  were  to  burn,  no  injury  of  any  impor- 
tance would  be  done  to  the  metalwork.  Such  fires  do  not  spread  rapidly 
and  are  readily  extinguished ;  but  when  a  plank  base  with  a  wooden  block 
pavement  thereon  catches  fire  on  a  windy  day,  disaster  is  almost  sure  to 
ensue. 

There  are  two  legitimate  ways  of  trimming  down  the  weight  of  metal  in 
the  floor-system  to  a  minimum,  viz.,  employing  nickel  steel  or  some  other 
alloy  for  the  metalwork,  and  supporting  the  cross-girders  at  intervals  by 
means  of  intermediate  trusses  and  cables.  In  adopting  the  first  expedient, 
care  should  be  taken  not  to  reduce  the  depths  of  the  joists  and  stringers 
below  the  limit  set  by  good  practice — otherwise  their  deflections  would  be 
great  enough  to  injure  the  pavement.  In  respect  to  the  second  expedient 
there  are  both  pros  and  cons  concerning  the  advisability  of  adopting  many 
lines  of  trusses  and  cables.     The  advantages  are  as  follows : 

First.     The  saving  in  weight  of  metal  in  the  cross-girders. 

Second.  The  reduction  in  cable  cross-section  due  to  the  lightening  of 
the  cross-girders. 

Third.  The  better  distribution  of  load  on  the  piers  with  its  conse- 
quent saving  of  both  shaft  masonry  and  base. 

Fourth.  The  lowering  of  the  grade  line  of  the  structure  (due  to  the 
shallowing  of  the  cross-girders),  with  its  consequent  reduction  in  cost  of 
climb  for  everything  that  crosses  on  the  structure. 

Fifth.  The  shortening  and  consequent  cheapening  of  the  approaches 
due  to  the  smaller  height  to  be  surmounted. 

The  disadvantages  are  as  follows: 

First.  The  somewhat  greater  weight  of  metal  due  to  the  larger  number 
of  parts  in  trusses,  cables,  and  steel  towers.  In  long,  heavy  spans  this 
really  is  not  a  disadvantage;  because,  on  account  of  ease  of  erection,  it 
often  pays  to  employ  comparatively  light  members 

Second.  The  somewhat  greater  total  width  of  deck  called  for  to  allow 
space  for  the  extra  trusses  and  cables;  but  this  is  often  not  disadvan- 
tageous, because  great  width  of  structure  is  necessitated  by  great  span- 
length. 

Third.  In  accordance  with  the  theory  of  probabilities,  the  more 
numerous  the  trusses  and  cables  the  greater  should  be  the  total  live  load 
per  lineal  foot  assumed  for  the  design;  for  witli  only  two  lines  of  cables, 
practically  the  entire  width  of  deck  must  be  loacUnl  in  order  to  produce 
the  maximum  stresses  in  either  cable,  while  with  sevei-al  lines  of  cables, 


ECONOMICS    OF    SUSPENSION    BRIDGES  265 

the  loading  of  a  much  smaller  width  of  deck  will  produce  maximum  stresses 
in  any  one  cable. 

The  next  economic  consideration  is  the  design  of  the  stiffening  trusses. 
It  must  be  remembered  that  the  weight  of  these  is  a  direct  function  of 
the  live  load  and  entirely  independent  of  the  dead  load,  which  passes 
immediately  from  the  floor  to  the  suspenders  and  cables  without  causing 
either  moment  or  shear  on  the  trusses.  It  is,  consequently,  expedient  to 
keep  the  live  load  down  to  the  lowest  legitimate  limit  consistent  with  the 
probable  loads  from  future  traffic. 

Custom  has  decreed  that  the  truss  depth  should  be  about  one-fortieth 
of  the  span  length,  but  a  greater  depth  would  reduce  the  weight  of  metal 
in  the  chords  without  increasing  materially  that  in  the  web.  It  is  claimed 
that  a  greater  depth  than  this  established  limit  would  not  be  aesthetic, 
but  this  can  be  determined  only  by  careful  study  for  each  case  as  it  arises. 

The  choice  of  panel  length  may  be  determined  from  the  standpoint  of 
aesthetics  or  by  an  economic  adjustment  between  floor-system  and  trusses. 
This  question  also  will  require  careful  study. 

The  system  of  cancellation  adopted  for  the  trusses  will  have  quite  a 
little  to  do  with  their  weights  of  metal,  but  the  consideration  of  appear- 
ance should  govern  in  this  matter.  If  a  single-intersection  truss  be 
adopted,  it  will  have  the  advantage  of  avoidance  of  ambiguity  in  stress  dis- 
tribution, but  it  will  not  provide  as  pleasing  an  appearance  as  will  the  double 
system  of  cancellation.  In  the  latter  the  vertical  posts,  as  far  as  the  ques- 
tion of  statics  is  concerned,  are  superfluous;  but  without  them  the  second- 
ary stresses  would  run  high,  the  connection  of  the  floor-beams  to  trusses 
would  be  awkward,  and  the  proper  attachment  of  the  trusses  to  the  cables 
would  be  difficult.  It  is  better,  therefore,  to  adhere  to  the  use  of  the  verti- 
cal posts  when  the  double-intersection  type  of  truss  is  selected.  These 
posts,  though,  may  be  made  of  minimum  section  consistent  with  their 
appearance  and  with  the  function  which  some  of  them  perform  in  distribu- 
ting the  load  to  the  cables. 

An  economic  point  of  importance  is  that  of  having  the  ends  of  stiffening 
trusses  free  or  anchored.  The  latter  condition  is  more  economic  of  metal 
in  chords,  but  there  is  little  or  no  difference  for  the  web ;  however,  it  neces- 
sitates extra  metal  and  expense  for  the  anchoring,  but  the  resultant  effect 
invariably  is  a  reduction  in  the  total  weight  of  metal,  and  hence  the  expe- 
dient should  generally  be  adopted. 

The  selection  of  the  versed  sine  for  the  cables  is  a  matter  of  economic 
importance.  Increasing  it  reduces  the  sectional  area  of  cables  and  back- 
stays, but  augments  sHghtly  their  lengths;  and  it  adds  to  the  height  and 
weight  of  the  tower  columns  and  their  bracing. 

On  the  other  hand,  it  effects  a  slight  saving  in  mass  and  cost  of  anchor- 
ages due  to  the  reduction  of  overturning  moment  that  is  caused  by  the 
diminution  of  stress  in  the  backstays.  Experience  has  shown  that  a  depth 
of  catenary  equal  to  one-ninth  of  the  span  will  usually  give  the  most  satis- 


266  ECONOMICS    OF   BRIDGEWORK  Chapter  XXIX 

factory  results;  but  there  is  no  hard-and-fast  rule  about  this,  and  it  is  per- 
missible to  use  any  depth  between  the  limits  of  one-eighth  and  one-tenth 
of  the  span.  In  the  past  the  author  had  never  tested  the  economics  of  this 
feature,  having  been  content  to  accept  the  dictum  of  experience  as  recorded 
in  engineering  text  books  and  hand  books;  but  in  connection  with  the 
special  investigations  prepared  for  this  treatise  and  the  late  economic 
studies  upon  which  it  is  so  largely  based,  a  number  of  estimates  have  been 
made  which  have  enabled  him  to  obtain  some  rough  figures  upon  the 
effect  of  increasing  the  depth  of  catenary. 

The  result  of  these  computations  appears  to  indicate  that  the  economic 
depth  for  cables  was  originally  adjusted  upon  the  basis  of  cariying  the 
masonry  piers  all  the  way  up  to  the  cable  carriages,  as  in  the  case  of  the 
first  East  River  bridge  known  as  the  Brooklyn  Bridge;  because  an  assumed 
increase  in  the  height  for  this  type  effected  no  economy.  But  in  the  case 
of  a  bridge  with  steel  towers  the  result  was  quite  different;  for  a  saving  of 
total  cost  was  indicated  when  the  depth  was  made  one-seventh  of  the  span- 
length.  That  is  probably  as  great  a  depth  as  a  proper  consideration  of 
appearance  would  permit. 

The  question  of  the  best  type  of  approaches  to  adopt  is  one  that  has 
to  be  settled  at  the  outset.  It  is  an  economic  one  in  most  cases,  but  occa- 
sionally the  local  conditions  or  the  matter  of  aesthetics  will  necessitate  a 
departure  from  the  economic  layout.  Briefly,  it  may  be  stated  that  the 
type  of  approach  which  costs  the  least  is  an  ordinary  trestle  or  viaduct 
entirely  independent  of  the  main  structure.  This  may  be  either  straight 
or  built  in  spiral  form,  as  there  is  but  little  difference  in  the  construction 
costs  of  the  two,  the  latter  generally  having  the  advantage  of  saving  in 
expense  for  right-of-way  and  property  damages.  Suspending  the  floor- 
system  or  stiffening  trusses  from  the  backstays  is  not  economic,  if  it  be 
practicable  to  build  a  trestle  approach;  and  even  if  it  is  not,  it  may  be 
better  to  substitute  short  spans  for  the  trestle,  supporting  them  at  intervals 
on  either  piers  or  rocker  bents,  the  depth  of  the  said  spans,  if  through  ones, 
being  made  the  same  as  that  of  the  stiffening  trusses  in  the  case  of  a  wire 
cable  structure,  or  of  any  convenient  or  economic  depth  in  the  case  of  an 
eye-bar-cable  bridge. 

The  uneconomics  of  suspending  the  floor  of  the  approaches  from  the 
backstays  are  as  follows: 

First.  The  far  greater  weight  of  metal  required  for  stiffening  trusses 
and  hangers  as  compared  with  that  for  the  trestle  approach,  the  item  of 
pedestals  for  the  latter  being  generally  a  bagatelle. 

Second.  The  far  greater  cost  of  the  anchorages  due  to  the  large  lever 
arm  for  the  overturning  moment,  the  cable  pull  being  horizontal  and  applied 
near  the  elevation  of  the  floor. 

The  only  case  in  which  it  is  economic  to  suspend  the  floor  of  the  ap- 
|)roachcs  from  the  backstays  is  when  there  is  deep  water  beneath  that 
is  required  for  navigation  purposes.     If  there  be  fairly  deep  water  that  is 


ECONOMICS   OF   SUSPENSION   BRIDGES  267 

not  needed  for  navigation,  the  best  type  of  approach  to  adopt  is  a  suc- 
cession of  deck  spans  of,  as  nearly  as  may  be,  economic  length. 

In  the  design  for  the  anchorages  there  is  a  fine  opportunity  for  bene- 
fiting from  economic  study.  There  are  three  general  cases  of  governing 
conditions  to  consider,  viz.,  foundations  on  bed  rock,  foundations  on  piles, 
and  foundations  on  clay  or  similar  material  without  piling.  If  the  bed  rock 
is  fairly  close  to  the  surface,  it  will  be  advisable  to  found  upon  it;  but 
otherwise  it  will  be  cheaper  to  put  in  shallow  foundations,  obtaining  the 
necessary  supporting  power  either  by  piling  or  by  spreading  the  base.  The 
maximum  of  economy  will  be  obtained  by  making  both  the  weight  of  ma- 
sonry in  the  rear  of  the  anchorage  and  the  foundation  area  in  the  front 
thereof  proportionately  as  large  as  practicable.  The  first  expedient  tends 
to  increase  the  resisting  moment  against  overturning,  and  the  second  to 
reduce  the  intensity  of  bearing  at  the  toe  of  the  face;  where,  of  course,  it  is 
greatest.  It  is  economic,  therefore,  to  make  the  anchorages  long  and 
narrow,  low  in  the  front  and  high  in  the  rear.  If  there  be  several  of  these 
in  the  form  of  walls — one  for  each  cable,  or  pair  of  cables, — instead  of  one 
solid  mass  of  concrete,  they  can  be  advantageously  connected  in  front  below 
the  ground  so  as  to  spread  the  base,  and  joined  in  the  rear  by  a  great  wall 
above  the  ground,  in  order  to  increase  the  weight  there. 

If  piles  be  employed,  they  should  be  driven  as  closely  together  as 
practicable  near  the  front  of  the  anchorage,  and,  if  it  be  found  advisable, 
spread  somewhat  near  the  rear  thereof — in  other  words  their  spacing  should 
be  adjusted  to  the  intensity  of  the  foundation  loading.  That  intensity 
should  be  made  as  nearly  uniform  as  possible  over  the  entire  base  by  the 
expedient  just  explained,  thus  avoiding  the  call  for  varied  spacing. 

With  a  single  exception,  the  preceding  considerations  cover  all  the 
important  economic  features  in  the  designing  of  suspension  bridges.  That 
exception  is  the  question  of  the  comparative  economics  of  wire  cables  and 
high-alloy-steel  eye-bar-cables,  concerning  which  hitherto  absolutely  noth- 
ing definite  has  been  known.  It  is  one  of  the  series  of  ten  major  economic 
problems  in  bridgework  that  in  1916  the  author  undertook  to  solve.  Its 
investigation  was  completed  in  March,  1920;  and  the  results  thereof,  as 
herein  previously  stated,  were  presented  two  months  later,  in  the  form  of  a 
memoir  to  the  Engineers'  Society  of  Western  Pennsylvania.  In  view  of  the 
fact  that  the  said  memoir  is  very  complete,  it  is  here  reproduced  verbatim 
as  follows: 

Comparative    Economics    of    Wire-Cables    and    High-Alloy-Steel 
Eye-bar-Cables  for  Long-Span  Suspension  Bridges 

The  economic  comparison  of  wire  cables  and  eye-bar  cables  for  sus- 
pension bridges  has  never  before  been  brought  to  the  attention  of  American 
engineers,  for  the  reason  that  comparatively  few  structures  of  the  sus- 
pension type  have  been  built  in  this  country.     Their  unsuitability  for 


268  ECONOMICS   OF   BRIDGEWORK  Chapter  XXIX 

railway  bridges,  excepting  those  of  exceedingly  long  span — far  longer  than 
any  that  have  been  constructed — and  the  slow  development  of  the  Amer- 
ican highway  system  have  combined  to  keep  the  type  in  the  background; 
but  the  time  is  approaching  when  it  will  be  necessary  to  carry  our  rapidly 
developing  network  of  highways  across  some  of  the  largest  of  our  rivers, 
and  then  the  suspension  bridge  may  have  an  opportunity  to  come  into  its 
own.  It  must  not  be  forgotten,  however,  that  the  conditions  warranting 
the  building  of  a  suspension  bridge  are  not  likely  to  be  often  encountered; 
because  it  is  nearly  always  the  fiat  of  the  War  Department  which  neces- 
sitates a  span-length  so  great  as  to  render  economical  the  building  of  a 
structure  of  that  type. 

By  means  of  a  long  and  elaborate  economic  investigation  made  in 
1918  and  published  in  1919  by  the  Western  Society  of  Engineers  under  the 
caption  "Comparative  Economics  of  Cantilever  and  Suspension  Bridges," 
the  author  has  shown  the  span-lengths  of  equal  cost  for  these  two  classes 
of  structure.  The  said  lengths  usually  vary  from  1,000  feet  for  liighway 
bridges  to  about  2,600  feet  for  steam-railway  bridges,  the  lengths  for  com- 
bined steam-railway  and  highway  structures  being  intermediate  and 
directly  interpolated  in  accordance  with  the  division  of  total  hve  load, 
including  impact  allowances,  between  railways  and  highways.  Later 
it  was  found  that  the  irregularity  of  the  abnormal  unit  prices  of  materials 
at  present  governing  has  lengthened  the  spans  of  equal  cost  some  two 
hundred  feet  for  highway  bridges  and  sixty  feet  for  steam-railway  bridges; 
but  a  return  to  normal  market  conditions  will  assuredly  bring  them  back 
to  about  the  Umits  first  found. 

Had  the  original  investigation  been  based  upon  the  assumption  of 
anchored  ends  instead  of  free  ends  for  the  stiffening  trusses,  the  span- 
lengths  for  equal  cost  would  have  been  found  about  one  hundred  feet 
shorter,  or  900  ft.  for  highway  bridges  and  2,500  ft.  for  railway  bridges  at 
ante-bellum  unit  prices,  and  1,100  ft.  for  highway  bridges  and  2,560  ft. 
for  railway  bridges  at  the  unit  prices  prevailing  early  in  1920. 

As  that  investigation  proved  that  the  suspension  bridge  is  less  econom- 
ical for  steams-railway  traffic  than  the  cantilever  structure  up  to  the 
extreme  practicable  main-span-length  of  the  latter,  and  as  it  is  well  known 
that  the  cantilever  is  always  the  superior  of  the  two  in  respect  to  the 
important  matter  of  rigidity,  the  present  investigation  has  been  limited 
to  the  consideration  of  highway  bridges  carrying  also  electric  railway 
trains,  such  as  those  that  cross  the  East  River  in  New  York  City. 

The  comparative  advantages  and  disadvantages  of  the  two  types  of 
cables  are  as  follows: 

First.  The  wires  for  the  cables  have  higher  clastic  limit  and  ultimate 
strength  than  can  proljably  ever  be  dc^velojiod  in  eye-bars. 

Second.  The  percentage  of  weight  of  details  is  far  lower  for  wire 
cables  than  for  eye-bar  cables. 

Third.     The  cost  of  erection  is  inevitably  less  for  wire  cables  than 


ECONOMICS   OF   SUSPENSION   BRIDGES  269 

for  eye-bar  cables,  because  with  the  former,  the  process,  while  tedious,  is 
not  at  all  complicated.  Before  the  erection  of  the  eye-bar  chains  is  begun, 
it  is  necessary  to  string  across  from  anchorage  to  anchorage  and  over  the 
tower  tops  several  lines  of  small  wire  cables.  These  have  to  be  used  in 
order  to  carry  the  first  few  lines  of  bars  until  the  latter  can  be  made  seK- 
supporting;  and  although  there  will,  of  course,  be  some  salvage  on  such 
erecting  cables,  their  use  will  be  quite  expensive.  Again,  as  the  eye-bars 
will  have  to  be  placed  on  the  pins  by  heating  and  shrinking,  it  is  evident 
that  the  process  is  necessarily  a  slow  one,  requiring  considerable  apparatus; 
hence  the  erection  cost  will  run  high.  The  total  cost  of  erection,  therefore, 
is  larger  for  the  eye-bar  cables  not  only  because  of  the  higher  unit  cost  of 
manipulation  but  also  on  account  of  the  greater  weight  of  metal  to  be  put 
in  place. 

Fourth.  The  lowest  point  in  the  catenary  of  the  wire  cables  can  be 
located  very  close  to  the  top  surface  of  the  deck,  thus  making  the  height 
and  the  cost  of  the  tower  columns  a  minimum.  Owing  to  the  necessity 
for  keeping  the  bottom  chords  of  the  crescent  trusses  above  the  elevation 
of  the  floor,  and  because,  for  a  fair  comparison,  the  center  lines  of  the  pairs 
of  eye-bar  cables  must  coincide  with  those  of  the  wire  cables,  it  is  necessary 
to  raise  the  tops  of  the  towers  several  feet,  thus  increasing  not  only  the 
cost  of  the  latter  but  also  the  length  and  cost  of  the  backstays. 

Fifth.  Wire-cable  bridges  do  not  call  for  special  wind  chords  for  the 
lateral  system;  but  in  eye-bar-cable  bridges,  owing  to  the  omission  of 
special  stiffening  trusses,  it  is  necessary  to  provide  such  chords;  and  this 
item  is  likely  to  be  quite  expensive. 

Sixth.  The  pound  price  of  the  wire  cables  is  comparatively  high,  being 
at  present  about  twice  as  great  as  that  for  eye-bar  cables  of  nickel  steel. 

Seve7ith.  The  attachment  of  the  wires  at  the  anchorages  is  both 
tedious  and  expensive,  whilst  that  of  the  eye-bars  is  simple  and  expeditious. 

Eighth.  The  wire  cables  require  stiffening  trusses;  but  the  two  tiers 
of  eye-bar  cables  are  in  tension  under  all  conditions  of  loading;  and  hence 
they  can  serve,  without  stiffening,  as  the  compression  chords  of  the  cres- 
cent trusses  which  are  formed  by  the  addition  to  them  of  vertical  posts 
and  adjustable  diagonals. 

Ninth.  There  is  an  uncertainty  in  respect  to  stress  distribution  in  the 
stiffening  trusses  of  the  wire-cable  bridge  that  does  not  exist  in  the  eye-bar- 
cable  structure,  although,  strictly  speaking,  the  adjustable  diagonals  in 
the  latter  involve  a  small  amount  of  ambiguity  in  the  division  of  the 
shear.  All  stresses  in  the  eye-bar-cable  bridges  can  be  determined  with 
accuracy  by  the  established  principles  of  statics,  v/hilst  those  in  the  stif- 
fening trusses  of  wire-cable  bridges  are  found  approximately  by  several  dif- 
ferent theories  based  upon  assumptions  which  are  sometimes  of  more 
than  doubtful  accuracy;  and,  consequently,  considerable  uncertainty 
concerning  the  maximum  stresses  to  be  provided  for  is  involved. 

To  as  great  an  extent  as  practicable,  all  of  these  governing  conditions 


270  ECONOMICS   OF   BRIDGEWORK  Chapter  XXIX 

have  been  duly  considered  in  making  the  economic  studies  for  the  prep- 
aration of  this  memoir. 

When  the  layout  of  the  investigation  for  the  solution  of  the  economic 
problem  herein  discussed  was  first  considered,  it  was  intended  to  make  the 
said  investigation  comparatively  short  by  confining  it  to  spans  of  only 
one  length  and  having  but  one  live  load.  That  span-length  was  1,750 
feet, — selected  because  it  was  used  by  the  author  in  his  preliminary  study 
of  the  proposed  crossing  of  the  Delaware  River  between  Philadelphia,  Pa., 
and  Camden,  N.  J.,  made  for  the  Camden  Bridge  Commissioners. 

The  proposed  structure  consisted  of  a  single  suspension  span  with 
backstays,  the  approaches  to  it  being  either  steel  or  reinforced-concrete 
trestlework,  entirely  independent  of  the  main  span.  The  deck,  in  a  later 
modification,  was  laid  out  for  a  double-track  electric  railway  at  the  middle, 
a  paved  roadway  supported  by  a  reinforced-concrete  base  twenty-two 
feet  wide  in  the  clear  on  each  side  thereof,  and  two  sidewalks,  each  ten 
feet  wide,  cantilevered  beyond  the  trusses,  of  which  there  were  four  lines. 
In  the  first  design  each  of  these  trusses  consisted  of  two  eye-bar  cables 
forming  two  crescents,  each  with  a  web  system  between  composed  of 
vertical  posts  and  adjustable  tension  diagonals,  but  later  there  was  also 
figured  a  wire-cable  structure  with  stiffening  trusses.  In  each  case  the 
towers  consisted  of  braced  steel  columns  with  segmental-roller  pedestals 
resting  on  concrete  shafts  supported  by  pneumatic  caissons  sunk  to  bed 
rock  at  a  depth  of  about  one  hundred  feet  below  low  water.  The  anchor- 
ages were  to  be  of  plain  concrete  either  supported  by  piles  driven  to  bed 
rock  or  else  resting  directly  on  a  foundation  of  satisfactorily-hard  material, 
should  such  be  encountered  when  making  the  borings.  Fig.  29a  gives 
the  layout  for  the  wire-cable  type,  and  Fig.  296  that  for  the  eye-bar-cable 
structure. 

The  first  set  of  calculations  prepared  for  this  paper  was  based  on  the 
preceding  data  and  consisted  of  five  designs  and  estimates  of  cost  of  fin- 
ished bridge  upon  the  following  lines : 

First.     Wire  cables  of  very  high  elastic  limit  and  ultimate  strength. 

Second.     Mayarl-steel  eye-bar-cables  having  an  elastic  limit  of  50,000 

lbs.  per  square  'nch  and  an  ultimate  strength  of  85,000  lbs.  per  square  inch. 

Third.     High-grade,  nickel-steel  eye-bar-cables  having  an  elastic  limit 

of  60,000  lbs.  per  square  inch  and  an  ultimate  strength  of  100,000  lbs.  per 

square  inch. 

Fourth.  Heat-treated,  alloy-steel  eye-bar-cables  having  an  elastic 
limit  of  at  least  75,000  lbs.  per  square  inch  and  an  ultimate  strength  of 
115,000  lbs.  per  square  inch. 

Fifth.  Heat-treated,  alloy-steel  cye-bar-cablcs  having  an  elastic  limit 
of  at  least  100,000  lbs.  per  square  inch  and  an  ultimate  strength  of  150,000 
lbs.  per  square  inch. 

The  specifications  used  for  the  designing,  as  far  as  they  would  apply, 
were  those  given  in  Chapter  LXXVIIl  of  "Bridge  Engineering,"  and  the 


ECONOMICS   OF   SUSPENSION   BRIDGES 


271 


intensities  of  working  stresses  for  the  wire  cables  were  60,000  lbs.  per  square 
inch  for  wire,  and  either  one-half  of  the  elastic  limit  or  one-third  of  the 


ultimate  strength  for  eye-bars,  the  lower  of  the  two  values  being  adopted. 
The  material  for  stiffening  trusses,  webs  of  crescent  trusses,  floor-systems, 
lateral  systems,  towers,  and  anchorages  was  assumed  to  be  commercial 


272  ECONOMICS   OF   BRIDGEWORK  Chapter  XXIX 

nickel  steel,  having  an  elastic  Hmit  of  55,000  lbs.  per  square  inch  and  an 
ultimate  strength  of  90,000  lbs.  per  square  inch. 

The  hve  loads  employed  were  as  follows: 

For  the  floor-system, 

Class  25  for  the  electric  railway, 
Class  B  for  the  roadways, 
Class  C  for  the  sidewalks. 

For  the  trusses  a  logical  combination  of  these  loads  was  adopted;  and 
a  ten-car  subway  train  was  assumed  on  each  track  when  figuring  the 
stiffening  trusses  of  the  wire-cable  structure  and  the  crescent  trusses  of 
the  eye-bar-cable  structure.  When  finding  the  moments  and  shears  for 
the  former,  in  order  to  give  the  wire-cable  bridge  the  best  possible  chance 
to  compete,  the  ends  of  its  stiffening  trusses  were  assumed  to  be  anchored 
down,  although,  of  course,  not  fixed,  and  the  theory  of  stress  determina- 
tion adopted  was  the  approximate  method  given  in  Johnson,  Bryan, 
and  Turneaure's  "Modern  Framed  Structures,"  Part  II,  instead  of  the 
older  method  of  Dr.  Wm.  H.  Burr,  which,  for  convenience  and  simphcity, 
was  taken  as  standard  by  the  author  in  writing  Chapter  XXVII  of  "Bridge 
Engineering."  The  results  of  the  two  theories  do  not  differ  greatly,  espe- 
cially for  ends  of  trusses  anchored,  but  the  latter  theory  requires  a  Kttle 
less  metal. 

In  order  to  ascertain  the  weights  of  metal  in  the  crescent  trusses,  there 
was  assumed  for  each  panel  point  a  load  of  unity;  and  its  effect  was  com- 
puted for  every  web  member  and  every  chord  member  thereof,  thus 
rendering  it  easy  to  find  all  the  Hve  load  stresses  and  dead  load  stresses  by 
means  of  the  sUde-rule.  These  index  stresses  were  checked  by  an  inde- 
pendent computer. 

After  the  first  set  of  computations  was  completed,  the  question  arose 
as  to  whether  the  assumption  of  a  double-deck  structure  carrying  a  much 
greater  proportion  of  electric-railway  live  load  would  have  caused  any 
material  changes  in  the  results;  and  it  was  decided  to  repeat  the  calcu- 
lations for  a  set  of  five  double-deck  structures.  The  result  indicated  no 
serious  disagreement,  as  is  shown  in  Table  29a. 

An  analysis  of  this  table  shows  how  very  little  variation  there  is  between 
single-deck  and  double-deck  bridges  in  respect  to  the  proportions  of  the 
various  materials  in  wire-cable  structures  and  the  corresponding  eye-bar- 
cable  structures.  For  this  reason  in  what  follows  the  author,  with  a  clear 
conscience,  has  drawn  his  general  conclusions  from  computations  on  single- 
deck  structures  only,  thus  saving  considerable  time  and  expense.  His 
so  doing  is  a  good  illustration  of  the  appHcation  of  the  "economics  of 
bridgework"  which  he  is  endeavoring  to  expound. 

The  investigations  made  up  to  this  point  permitted  the  estabhshment 
of  a  number  of  formulse  for  quantities  of  materials  involving  variations  in 
span  length  and  loading,  thus  permitting  of  an  extension  of  the  study 


ECONOMICS   OF  SUSPENSION  BRIDGES 


273 


without  a  seriously  great  augmentation  of  labor  and  expense.  These 
formulae  are  strictly  logical  in  form.  They  were  derived  on  a  theoretical 
basis,  the  coefficients  thus  determined  being  changed  a  few  per  cent, 
where  necessary,  to  agree  with  the  computed  weights  for  the  various 
structures  which  had  been  worked  out  completely.  It  was,  therefore, 
decided  to  compute  and  record  quantities  for  shorter  and  longer  spans  in 
order  to  prepare  curves  giving,  for  all  practicable  span-lengths,,  the  quan- 
tities of  all  materials  per  lineal  foot  of  main  span. 

TABLE  29a 
Ratio  of  Quantities  of  Materials  in  Eye-bar-cable  Bridges  to  those  in 

Wire-cable  Bridges. 


Ratios 

Elastic 

Limits 

of 

Eye-bars 

Cables 

Nickel  Steel 

Anchorages  and 
Pier  Shafts 

Pier  Bases 

Single 
Deck 

Double 
Deck 

Single 
Deck 

Double 
Deck 

Single 
Deck 

Double 
Deck 

Single 
Deck 

Double 
Deck 

50,000 

60,000 

75,000 

100,000 

3.76 
2..  82 
2.05 
1.42 

3.75 
2.82 
2.05 
1.41 

0.73 
0.68 
0.65 
0.63 

0.69 
0.66 
0.62 
0.60 

1.09 
1.03 
0.99 
0.94 

1.08 
1.02 
0.98 
0.93 

1.16 
1.06 
1.00 
1.00 

1.15 
1.08 
0.96 
0.88 

The  formulae  referred  to  are  the  following: 
Wire  Cable  Bridges. 
Stiffening  Trusses. 

Weight  of  One  Chord: 

Effect  of  Live  Load  Reversal  Neglected, 

Wc=O.Q9^(o.8^4:~),  but  not<0.09^^ 
sd\  Lt  J  sd 

Fifty  Per  Cent  of  Reversal  Stress  Added  to  Main  Stress, 

TFc=0.12^fo.9+1.5^Vbutnot<0.12^. 

sd  \  Lt  J  sd 

Seventy  Five  Per  Cent  of  Reversal  Stress  Added  to  Main  Stress, 

Tfc  =  0. 132^(0. 92+1.1^),  but  not<0. 132=^. 
sd\  Lt  J  sd  ■ 

Weight  of  Web  Members : 
Pratt  System. 

Effect  of  Live  Load  Reversal  Neglected, 

TF^  =  0.83 —  - — z =2.5 —  for  p  =  d. 

s  \     dp     /  s 


274  ECONOMICS   OF  BRIDGEWORK  Chapter  XXIX 

Fifty  Per  Cent  of  Reversal  Stress  Added  to  Main  Stress. 

,^„=1.25^(?^)=3.75^forp  =  d 
s  \     dp     /  s 

Seventy-five  Per  Cent  of  Reversal  Stress  Added  to  Main  Stress. 

Tr„  =  1.46^(?^)  =4.38^' for  ,  =  d. 

Warren  System,  Single  or  Double-Cancellation,  with  Verticals. 
Effect  of  Live  Load  Reversal  Neglected, 

Tf „  =  0.83 ^'(?^ii^)  =2. 1  ^  for  p=d. 
Fifty  Per  Cent  of  Reversal  Stress  Added  to  Main  Stress. 

Tr„=1.25^(P^±l^)  =3.12^' for  p=d. 
Seventy-five  Per  Cent  of  Reversal  Stress  Added  to  Main  Stress. 

H.„=1.46W?!^±^)  =3.65^  for  p  =  d. 

Notation. 

i  =  Main  span  length  in  feet; 
d  =  Depth  of  stiffening  truss  in  feet; 
p  =  Panel  length  of  stiffening  truss  in  feet; 
i  =  Transverse  distance  between  chords  carrying  wind  stresses; 
L  =  Live  load  in  pounds  per  lineal  foot  of  truss; 
i/;  =  Transverse  wind  load  in  pounds  per  lineal  foot  of  bridge; 
s  =  Working  stress  in  tension,  in  pounds  per  square  inch; 
Trc  =  Weight  of  one  chord  in  pounds  per  hneal  foot; 
Wto  =  Weight  of  web  members  in  pounds  per  lineal  foot  of  truss. 

Main  Cables. 
Weights : 

rs—QAoL-^  sec  B  j 

V 
„        0.45^2  sec  5  Y  _    ._„,        _, 

rs— 0.45i^  sec  5-j- 

For 

r/l  =  i  sec  B  =  1 .094,  r/l  =  1 .  032; 


ECONOMICS  OF  SUSPENSION  BRIDGES  275 

Notation. 

I  =  Main  span  length  in  feet. 

V  =  Length  of  cable  of  central  span  in  feet, 
r  =  Rise  of  cable  in  feet. 

B  =  Angle  of  inclination  of  cable  at  tower. 
Ds  =  Superimposed  dead  load  in  pounds  per  Kneal  foot  of  bridge 

(exclusive  of  weight  of  cable). 
L  =  Live  load  in  pounds  per  lineal  foot  of  bridge, 
s  =  Working  tensile  stress  in  cable  in  pounds  per  square  inch. 
TF  =  Weight  of  cable  in  pounds  per  foot  of  cable. 

V  . 

TF  -T= Weight  of  cable  in  pounds  per  lineal  foot  of  bridge. 

r     1 
Eye-bar  Cable  Bridges,  for  t^k- 


Weight  of  Eye-bars  in  Main  Span. 


TF.=    '■'' 


s-5.21 


A+L(0.44    ^^ 


lOOd 


)]• 


Weight  of  Web  Members  of  Cable. 

T7^=1.7— fo. 8+0.2 ^V  but  not  <1.7— . 

Notation. 

I  =  Length  of  main  span  in  feet, 
r  =  Rise  of  cable  in  feet. 
d  =  Maximum  depth  of  crescent  truss  in  feet. 
p  =  Panel  length  of  crescent  truss  in  feet. 
Ds  =  Superimposed  dead  load  in  pounds  per  lineal  foot  of  bridge 
(exclusive  of  weight  of  eye-bars,  but  including  weight  of 
web  members  of  cable). 
L  =  Live  load  in  pounds  per  lineal  foot  of  bridge. 
s  =  Working  stress  in  tension  in  pounds  per  square  inch. 
We  =  Weight  of  eye-bars  in  pounds  per  lineal  foot  of  bridge. 
TFjo= Weight  of  web  members  of  crescent  truss,  in  pounds  per 
lineal  foot  of  bridge. 

The  span-length  selected  for  the  low  limit  of  the  computations  was 
1,200  feet,  and  that  for  the  high  limit  thereof  was  2,300  feet,  thus  giving 
for  all  diagrams  three  points  through  which  to  pass  each  curve.  Ordinarily, 
it  is  not  safe  to  plot  a  curve  through  three  points  only;  but  in  this  case 
there  were  at  hand  several  similar  curves  for  suspension  bridges  estab- 
lished previously  by  the  author  for  another  economic  investigation,  hence 
no  mistake  was  made  in  the  plotting. 

The  results  of  the  computations  are  shown  in  Figs.  29c,  29d,  and  29e. 
In  Fig.  29c  are  recorded  on  four  separate  diagrams  the  quantities  of  the 
various  materials  for  wire-cable  bridges  of  span-lengths  varying  from 


276 


ECONOMICS   OF   BEIDGEWORK 


Chapte.r  XXIX 


1,000  feet  to  3,000  feet.  The  curves  are  for  single-deck  structures;  but 
the  quantities  found  for  the  double-deck  structures  of  1,750  feet  span  are 
shown  by  short  dotted  lines.  In  Fig.  29d  are  indicated  in  a  similar  manner 
the  weights  of  metal  per  lineal  foot  of  main  span  for  alloy-steel  eye-bars  in 
bridges  of  that  type;    and  in  Fig.  29e  are  recorded  correspondingly  the 

/ZC       /?00      AW        /SOO       /8a)       20(y}       2200       2400       dSCO       ^(O       306O 


StXO 


/tXOJ 


ajoo 


6000 


?0(XO 


&X0 


-/eooa 


i^OOOi 


/aoo      /600      jax>      2CW      2ax>      zaoo 

ia/y^  of  Cenf-ra/    Span    rn  fief- 


Z600 


2303       JOOO 


Pig.  29c.     Quantities  for  Wire-Cable  Suspension-Bridges. 

quantities  of  nickel  steel,  concrete  in  shafts  and  anchorages,  and  mass  of 
materials  in  pier  bases  for  such  structures. 

In  order  to  illustrate  the  manner  of  using  these  diagrams  and  at  the 
same  time  to  draw  therefrom  conclusions  conceniing  the  ]-)resent  status  of 
the  economics  of  the  two  types  of  cable  under  discussion,  it  will  be  wcU  to 


ECONOMICS   OF   SUSPENSION   BRIDGES 


277 


solve  several  examples  based  on  current  unit  prices  of  the  materials  in 
place.     These  may  be  taken  as  follows: 

Wire  Cables 23^  per  lb 

Mayan  steel 10^     " 

Commercial  nickel  steel 11^     " 

High-grade  nickel  steel 12^     ' ' 

Concrete  in  pier  shafts  and  anchorages .  .  $16.00  per  cu.  yd. 

Mass  of  pneumatic  bases $35.00    "       " 

^'^ /-^^  .   -^^     /«!?     /av    jaxi     2ZX)     sw     3500     zsoo    Jtm 


/ceo        /2X)        AW       /SCO        J&OO       3XX>       2200       2W       2500        2900    '  30tX) 
Ljsnffff}  a^  Cenfraf  3pan  rn  Feef 

Fig.  29d.     Weights  of  Alloy-Steel  Eye-bars  in  Eye-bar-Cable  Suspension-Bridges. 

In  pitting  the  eye-bar-cables  of  the  various  alloy-steels  against  wire 
cables  it  will  suffice  to  figure  for  three  spans,  viz.,  those  of  1,000,  2,000,  and 


278 


ECONOMICS   OF   BRIDGEWORK 


Chapter  IQOX 


3,000  feet.  Attention  is  called  to  the  fact  that  the  costs  found  per  foot  of 
main  span  are  not  total  for  the  structures;  because  the  items  of  costs  of 
deck  and  floor-system,  being  the  same  for  both  types,  have  been  omitted 
for  the  sake  of  simphcity.     The  lateral  system,  though,  has  been  taken 


sm 


SSCOJ 


=^mo 


JQW 


3X0 


1000        JZOO 


/6C0        /800       ZOOO       Z20Q       ZW 
Length  of  Csnfra/  ^san  /n  Feet- 


2S00       2dX)       3000 


Fig.  29e.    Quantities  of  Various  Materials  in  Eye-bar-Cable  Suspension- Bridges, 

into  account,  because  the  weights  of  metal  thereof  in  the  two  types  of 
structure  differ  materially.  The  principal  reason  for  this  is  that,  in  the 
eye-bar  type,  special  wind  chords  will  be  obhgatory;  whilst,  in  the  wire- 
cable  type,  the  chords  of  the  Htiffciiing  trusses  serve  as  wind  chords,  only  a 
small  increase  in  sections  above  those  needed  for  live  loads  being  required. 


ECONOMICS   OF   SUSPENSION   BRIDGES  279 

MAYARf  Steel  Comparison. 
1,000-Foot  Span. 

From  Fig.  29c  we  can  make  for  the  wire-cable  structm-e  the  follow- 
ing estimate: 

Wire  cables ........  4,300  lbs.  @  23^     =  $989 .  00 

Nickel  steel. ......  .  12,200    "  @  lU     =  1,342.00 

Plain  concrete 94  cu.  yd.  @  $16.00=  1,504.00 

Mass  of  bases 28     "  @  $35.00=       980.00 

Total  . =  $4,815.00 

From  Figs.  29d!  and  29e  we  have  for  the  Mayari  steel  the  following 
estimate. 

Mayari  steel.  ......   14,400 lbs.  @     10^     =  $1,440.00 

Nickel  steel 8,600    ''    @     lU     =       946.00 

Plain  concrete 98  cu.  yds.  @  $16 .  00  =    1,568 .  00 

Mass  of  bases 28     "         @  $35.00=       980.00 

Total .....,......=  $4,934.00 

2,000-Foot  Span. 

wire-cable  structure 

Wire  cables.  . 8,500 lbs.  @     23^     =  $1,955.00 

Nickel  steel 18,000   ''  @     lU     =    1,980.00 

Plain  concrete 89  cu.  yds.  @  $16 .  00  =    1,424 .  00 

Mass  of  bases 17     "  @  $35.00=       595.00 

Total =  $5,954.00 

EYE-BAR-CABLE    STRUCTURE 

Mayan'  steel 33,600  lbs.  @  10(2^     =  $3,360 .  00 

Nickel  steel 13,800    "  @  11^     =    1,518.00 

Plain  concrete 100  cu.  yds.  @  $16 .  00  =    1,600 .  00 

Mass  of  bases 22     ''  @  $35.00=       770.00 

Total =$7,248.00 

From  these  four  estimates  it  is  evident  that  at  present  prices  untreated 
Mayari-steel  eye-bar-cables  cannot  compete  with  wire  cables  in  suspension 
bridges.  With  the  shortest  economic  span-length  for  highway  suspension 
bridges,  viz.,  1,000  feet,  in  order  to  compete  with  wire,  the  untreated 
Mayari  steel  would  have  to  be  put  in  place  at  a  pound  price  of  less  than 
9.2  cents.  While  this  could  probably  be  done  without  actual  loss,  it  can 
readily  be  seen  that,  in  general,  untreated  Mayari-steel  eye-bars  cannot 
be  employed  economically  for  suspension-bridge  cables. 


280  ECONOMICS   OF  BKIDGEWORK  Chapter  XXIX 

As  heat-treated,  carbon-steel  eye-bars  have  an  elastic  limit  of  50,000 
lbs.  per  square  inch,  the  same  as  that  for  untreated  Mayari-steel  eye-bars, 
and  as  the  unit  price  erected  is  also  about  the  same,  the  conclusions  reached 
concerning  the  latter  will  apply  also  to  the  former. 

As  for  heat-treated,  Mayari-steel  eye-bars,  the  author  has  no  data 
regarding  their  strength,  nor  is  he  conviflced  that  the  irregularity  in  the 
elastic  limit  of  that  alloy  would  not  militate  too  strongly  against  using  it 
in  bridgework  after  heat  treatment.  Judging,  though,  from  the  com- 
putations which  follow  concerning  heat-treated  nickel-steel  eye-bars,  one 
would  surmise  that  suspension  bridges  of  heat-treated,  Mayari-steel  eye- 
bars  might  be  economical  up  to  spans  of  2,000  feet, 

High-Grade  Nickel-Steel  Comparison. 
1,000-Foot  Span. 

EYE-BAR-CABLE    STRUCTURE 

Eye-bar  cables 11,400 lbs.  @     12^     =  Sl,368.00 

Nickel  steel 8,300"  @     11^     =       913.00 

Plain  concrete. .....  94  cu.  yds.  @  $16 .  00  =    1,504 .  00 

Mass  of  bases 27     "  @  $35.00=       945.00 

Total =  $4,730.00 

2,000-Foot  Span. 

Eye-bar  cables 24,600 lbs.  @     12^     =  $2,952.00 

Nickel  steel 12,800"     @     lU     =    1,408.00 

Plain  concrete 94  cu.  yds.  @  $16.00=    1,504.00 

Mass  of  bases 20     "  @  $35.00=       700.00 

Total .,.,.,..    =  $6,564.00 

A  comparison  of  these  figures  with  those  previously  made  for  wire- 
cable  structures  shows  that  the  high-grade,  untreated,  nickel-steel  is 
economic  .for  1,000-ft.  spans  but  not  for  those  of  2,000  feet,  hence  let  us 
test  for  an  intermediate  length. 

1,500-Foot  Span. 

WIRE-CABLE    STRUCTURE 

Wire  cables 6,400  lbs.  @     23^^     =  $1,472 .  00 

Nickel  steel 15,000   "  @     11^     =    1,650.00 

Plain  concrete 88  cu.  yds.  @  $16.00=    1,408.00 

Mass  of  bases 20      ''  @  $35.00=       700.00 

Total =  $5,230.00 


ECONOMICS   OF   SUSPENSION   BRIDGES  281 

EYE-BAR-CABLE    STRUCTURE 

Eye-bar  cables 17,300 lbs.  @     12^     =  $2,076.00 

Nickel  steel 10,100   "  @     lU     =    1,111.00 

Plain  concrete 90  cu.  yds.  (a)  $16 .  00  =    1,440 .  00 

Mass  of  bases 20     "  @  $35.00=       700.00 

Total =  $5,327 .00 

From  these  figures  it  is  seen  that  untreated,  high-grade,  nickel-steel 
eye-bars  can  compete  today  with  wire  cables  for  span-lengths  below  about 
1,400  feet.  If  they  were  heat-treated,  their  intensities  of  working  stress 
could  probably  be  made  as  high  as  40,000  lbs.  per  square  inch,  correspond- 
ing to  an  elastic  limit  of  80,000  lbs.  or  an  ultimate  strength  of  120,000  lbs. 
The  value  of  these  eye-bars  in  place  would  be  13  cents  per  lb. 

Heat-Treated  Nickel-Steel  Comparison 

2000-Foot  Span. 

eye-bar-cable  structure 

Eye-bar  cables  ......  16,100  lbs.  @  13^     =  $2,093 .00 

Nickel  steel. 11,900    "     @  11^     =    1,309.00 

Plain  concrete. . . 87  cu.  yds.  @  $16.00=    1,392.00 

Mass  of  bases.......  18      "         @  $35.00=      630.00 

Total. =$5,424.00 

This  is  considerably  less  than  the  cost  previously  found  for  a  wire-cable 
structure,  consequently  let  us  test  for  a  2,500-ft.  span. 

2500-Foot  Span. 

WIRE-CABLE    STRUCTURE 

Wire  cables .........  10,800  lbs.  @    23^     =  $2,484 .  00 

Nickel  steel 21,400    "     @     11^     =2,354.00 

Plain  concrete. 97  cu.  yds.  @  $16.00=    1,552.00 

Mass  of  bases 19      ''        @  $35.00=      665.00 

Total =$7,055.00 

EYE-BAR-CABLE    STRUCTURE 

Eye-bar  cables 21,000  lbs.  @     13^     =$2,730.00 

Nickel  steel 14,800    "     @     11^     =    1,628.00 

Plain  concrete 98  cu.  yds.  @  $16 .  00  =    1,568 .  00 

Massofbases ...20       '*         @  $35.00=      700.00 

Total =$6,626.00    ' 


282  ECONOMICS   or   BRIDGEWORK  Chapter  XXIX 

From  these  assumed  figures  it  appears  that  heat-treated,  high-grade, 
nickel-steel  eye-bars  could  probably  be  used  economically  for  suspension- 
bridge  spans  up  to  at  least  3,000  feet. 

It  is  within  the  realm  of  possibility  that  in  a  few  years  there  will  be 
manufactured  heat-treated,  chrome-molybdenum-steel  eye-bars  having  an 
ultima,te  strength  of  150,000  lbs.  per  square  inch,  for  which  the  intensity  of 
working  stress  may  be  taken  at  50,000  lbs.  per  square  inch,  corresponding  to 
a  minimum  elastic  limit  of  100,000  lbs.;  and  that  the  metal  in  place  will 
be  worth  not  to  exceed  15  cents  per  lb. 

Let  us  test  this  for  a  3,000-ft.  span, 

Heat-Treated  Chrome-Molybdenum-Steel  Comparison 
dOOO-Foot  Span. 

WIRE-CABLE    STRUCTURE 

Wire  cables 13,400  lbs.  @  23^^     =  $3,082 .  GO 

Nickel  steel 25,000    "     @  llj!^     =2,750.00 

Plain  concrete 112  cu.  yds.  @  $16.00=    1,792.00 

Mass  of  bases 25       "        @  $35.00=      875.00 

Total =$8,499.00 

EYE-BAR-CABLE    STRUCTURE 

Ey^^bar  cables 19,000  lbs.  @     15cf     =  $2,850 .  00 

Nickel  steel 17,200    "    @     n</^     =   1,892.00 

Plain  concrete 110  cu.  yds.  @  $16.00=    1,760.00 

Mass  of  bases 22''       "    @  $35.00=      770.00 

Total =$7,272.00 

From  these  figures  it  is  ex'ident  that  the  hypothetical  "Chromol"  steel 
at  the  hypothetical  pound  price  used  would  be  much  more  economical  than 
wire  for  suspension  bridges  of  all  possible  span  lengths. 

Resume  of  Findings 

Summarizing  the  results  of  the  entire  investigation,  on  the  basis  of 
present  unit  prices,  the  following  conclusions  are  reached. 

Fird.  Neither  untreated  Mayari-steel  eye-bars  nor  heat-treated  car- 
bon-steel eye-bars  can  compete  with  wire  in  the  building  of  highway  sus- 
pension bridges. 

Second.  If  Mayari-stecl  eye-bars  after  being  hoat-ti-eated  arc  reliable 
and  satisfactory,  it  is  not  unlikely  that  they  can  compete  with  wire  cables 
for  spans  up  to  2,000  feet. 

Third.  Untreated  eye-bars  of  high-grade  nickel-steel  are  more  eco- 
nomic than  wire  for  spans  up  to  1,400  feet. 


ECONOMICS   OF   SUSPENSION   BRIDGES  283 

Fourth.  Heat-treatod  eye-bars  of  high-grade  nickel-steel  are  probably 
economic  for  all  spans  less  than  3,000  feet. 

Fifth.  If  satisfactory  eye-bars  can  be  made  of  heat-treated  "  Chromol " 
steel,  and  having  an  elastic  limit  exceeding  100,000  lbs.  per  square  inch  and 
an  ultimate  strength  of  not  less  than  150,000  lbs.  per  square  inch,  they  will 
be  more  economical  than  wire  cables  for  suspension  bridges  of  any  feasible 
span-lengths. 


CHAPTER  XXX 


ECONOMICS    OF   MOVABLE    SPANS' 


In  dealing  with  the  economics  of  movable  spans  it  will  suffice  to  con- 
sider only  those  types  thereof  which  have  survived  the  test  of  time,  rele- 
gating the  others  to  oblivion.  The  description  and  history  of  all  such 
types,  good,  bad,  and  indifferent,  will  be  found  in  Chapters  XXVIII  to 
XXXI,  inclusive,  of  "Bridge  Engineering."  As  stated  there,  the  surviving 
types  are  the  swing,  the  bascule,  and  the  vertical  hft;  and  the  first  men- 
tioned, as  will  be  shown  further  on  in  this  chapter,  has  no  longer  any  real 
raison  d'etre.  The  choice  today,  consequently,  is  between  the  bascule  and 
the  vertical  lift,  with  the  preponderance  of  advantage  and  economy  in  most 
cases  favoring  the  latter. 

Before  beginning  a  discussion  of  the  comparative  costs  of  the  three 
surviving  types,  it  will  be  well  to  consider  thoroughly  all  their  important 
advantages  and  disadvantages,  excepting  only  those  that  relate  to  first 
cost  of  construction,  plus  capitalized  cost  of  maintenance  and  repairs. 

Swing-Span  versus  Either  Bascule  or  Vertical  Lift 

First.  The  swing  provides  two  openings,  while  either  the  bascule  or  the 
vertical  lift  affords  only  one.  This  is  claimed  by  the  advocates  of  the  swing 
as  an  advantage;  but  it  is  not  often  such,  because  very  seldom  is  there  a 
location  at  which  there  exists  a  possibihty  of  the  water  traffic  being  so  great 
as  to  necessitate  the  simultaneous  passage  of  vessels  in  opposite  directions, 
or  such  a  large  amount  thereof  in  one  direction  as  to  call  for  two  openings. 
Probably  not  one  location  in  a  hundred  would  have  so  many  craft  passing 
that  two  openings  would  be  utilized  at  the  same  time,  excepting  semi- 
occasionally.  But  if  such  were  the  case,  the  single  opening  could  be 
enlarged  so  as  safely  to  permit  two  vessels  to  pass  at  the  crossing.  The 
question  would  then  arise  as  to  how  greatly  the  single  opening  should  be 
increased  in  order  to  afford  equal  facility  for  passing,  as  compared  with  a 
structure  having  two  openings.  In  the  authoi-'s  opinion,  if  the  single 
opening  in  ordinary  cases  were  made  twenty-five  per  cent  wider  than  either 
opening  of  the  swing,  the  facility  thus  provided  for  the  simultaneous  pas- 


*  This  chapter  was  presented  as  a  memoir  to  the  American  Railway  Engineering 
Association  in  Dec,  1920,  and  is  now  due  to  ai)pear  in  its  "Proceedings."  It  will  be 
submitted  to  the  leading  bridge  engineers  of  this  country  (both  in  and  outside  of  the 
Association)  for  a  thorough  discussion. 

284 


ECONOMICS   OF  MOVABLE   SPANS  285 

sage  of  two  vessels  woukl  not  bo  inferior;  but  for  small  openings,  of  course, 
this  percentage  of  increase  would  have  to  be  much  greater. 

Second.  The  swing,  on  account  of  either  its  pivot  pier  or  its  draw  pro- 
tection, offers  much  more  obstruction  to  the  flow  of  water  than  does  either 
of  the  other  types. 

Third.  The  cost  of  maintenance  is  more  in  a  swing  span  than  in  either 
of  the  others  on  account  of  the  upkeep  and  periodical  replacement  of  a 
costly  and  perishable  drawn  protection. 

Fourth.  The  swing,  of  necessity,  occupies  space  outside  of  that  required 
for  the  accommodation  of  land  traffic,  while  the  other  types  do  not. 

Fifth.  The  least  practicable  time  of  operation  is  usually  twice  or  thrice 
as  great  for  a  swing  as  for  a  corresponding  single-leaf  bascule  or  vertical 
lift. 

Sixth.  Either  the  vertical  lift  or  the  single-leaf  bascule  affords  better 
automatic  adjustment  of  the  railroad  tracks  thereon  than  does  the  swing 
span. 

Seventh.  In  the  case  of  future  enlargement  of  bridge  to  accommodate 
an  increase  of  traffic,  the  swing  has  to  be  torn  down  and  rebuilt,  but  a 
vertical  Hft  or  a  bascule  can  simply  be  duplicated  alongside. 

Eighth.  The  danger  of  the  span's  being  struck,  when  in  motion,  by 
passing  vessels  is  much  greater  in  the  case  of  a  swing  than  in  that  of  either 
of  the  other  types. 

Ninth.  The  wider  the  roadway  of  a  swing  the  more  obstructive  does 
it  become  to  navigation,  whilst  the  widening  of  either  a  vertical  lift  or  a 
bascule  does  no  harm  thereto  whatsoever. 

Tenth.  In  passing  vessels  with  low  masts,  a  swing  has  to  open  just  as 
fully  as  for  a  high-masted  craft,  which  is  not  the  case  with  a  vertical  lift 
or  a  bascule. 

Eleventh.  In  sand-bearing  streams  the  protection-works  for  the  mov- 
ing span  of  a  swing  bridge  cause  a  deposit  of  sediment,  and  thus  often  tend 
to  obstruct  navigation. 

Twelfth.  In  the  case  of  a  shifting  channel,  the  two  openings  in  a  swing 
may  score  an  advantage  for  that  type  over  the  other  types,  in  that  vessels 
might  be  able  to  pass  through  one  opening  after  the  other  has  been  silted 
up;  but  under  such  conditions  the  silting  is  more  than  likely  to  block  both 
openings.  Moreover,  for  such  conditions  the  vertical  Hft  is  far  superior 
to  the  other  two  types,  in  that  the  design  of  the  structure  can  be  made  so 
as  to  raise  at  any  time  any  one  of  several  similar  spans,  simply  by  shifting 
thereto  the  towers,  the  machinery,  and  the  house  or  houses. 

Vertical  Lift  versus  Bascule 

Comparing  the  vertical  lift  with  the  bascule,  the  former  has  several 
.  advantages,  amongst  which  may  be  mentioned  the  following : 

First.     The  floor  is  always  horizontal,  permitting  the  employment  of 


286  ECONOMICS   OF   BRIDGEWOEE:  Ch.^pter  XXX 

any  type  of  deck  that  can  be  used  on  a  fixed  span,  which  is  not  the  case 
for  a  bascule.  That  type  of  movable  span  necessitates  a  tunber  deck  with 
its  consequent  fire-risk. 

Second.  Great  wind  pressuj-e  during  operation  has  no  appreciable  effect 
on  a  vertical  Hft,  while  it  may  cause  serious  delay  to  a  bascule,  or  even, 
under  extreme  conditions,  prevent  its  operation  altogether. 

Third.  The  vertical  lift  does  not  have  to  rise  so  high  for  low-masted 
passing  craft  as  does  the  bascule;  and  thus  it  saves  a  considerable  amount 
of  time  and  power. 

Fourth.  In  railroad  bridges  when  the  moving  span  is  down,  it  acts 
just  like  any  fixed  span,  as  far  as  operation  under  traffic  is  concerned,  which 
cannot  be  said  for  either  the  swing  or  the  double-leaf  bascule;  or,  in  other 
words,  for  railroad  trafiic  the  vertical  hft  is  the  most  rigid  of  the  three  types, 
excepting  only  in  the  case  of  the  single-leaf  bascule,  which  is  usualty  quite 
rigid. 

Fifth.  In  case  of  a  shifting  channel,  it  is  feasible  to  make  a  number  of 
the  spans  alike  and  to  arrange,  for  any  time  in  the  future  and  at  com- 
paratively moderate  expense,  to  have  the  towers  and  machinery  taken 
down,  transferred,  and  re-erected,  so  as  to  lift  any  one  of  the  said  like 
spans.  This  could  not  by  any  possibihty  be  done  in  the  case  of  any  other 
type  of  movable  structure. 

Sixth.  The  vertical  lift,  when  its  towers  do  not  rest  on  flanking  spans, 
lends  itself  readily  to  a  future  raising  or  lowering  of  the  grade  fine  in  a  way 
that  no  other  type  of  movable  span  can  possibly  do;  for  all  that  is  neces- 
sary is  to  change  the  elevation  of  the  bearings  of  the  hft  span.  If  a  change 
of  grade  be  anticipated  when  the  plans  are  being  prepared,  provision  should 
be  made  therefor  by  increasing  adequately  the  heights  of  the  towers;  but 
if  at  any  time  the  grade  on  a  vertical-hft  bridge  of  the  type  mentioned,  for 
which  no  such  preparation  has  been  made,  has  to  be  raised  to  such  an 
extent  that  there  will  be  interference  because  of  the  counterweights  reaching 
the  new  decks  of  the  approaches  in  the  towers,  the  result  desired  could  be 
accomplished  by  arranging  for  a  small  portion  of  the  said  approaches  to 
move  either  laterally  or  vertically  out  of  the  way  of  the  counterweights, 
whenever  a  very-tall-masted  vessel  has  to  pass.  For  any  other  vessel,  how- 
ever, these  moving  approaches  would  not  have  to  be  utiHzed ;  consequently, 
they  would  seldom  need  to  be  operated. 

Seventh.  The  vertical  lift  accommodates  itself  to  a  skew  crossing  far 
better  than  does  the  bascule,  as  in  the  latter  the  tail  has  to  be  squared, 
while  in  the  former  both  the  span  and  the  towers  maj^  be  skewed,  thus 
reducing  the  clear  waterway  (and  consequently  the  length  of  moving 
span)  to  a  minimum. 

Eighth.  By  spanning  the  opening  between  tops  of  towers  in  a  vertical- 
lift  bridge,  electric-wires,  water-pipes,  and  gas-pipes  can  be  caiTiod  across; 
but  the  accomplishment  of  this  in  the  case  of  a  bascnk^  or  a  swing  would 


ECONOMICS    OF   MOVABLE    SPANS  287 

necessitate  either  expensive  and  troublesome  submarine  cables  and  con- 
duits or  special  towers  for  carrying  an  overhead  span. 

Ninth.  The  inherent  simphcity  of  the  vertical  lift  as  a  piece  of  mechan- 
ism, compared  with  the  bascule,  makes  it  more  reliable  in  operation,  and, 
on  that  account,  somewhat  less  expensive.  For  this  reason  the  vertical 
lift  would  have  an  advantage  over  the  bascule  in  many  foreign  countries, 
such  as  those  of  Latin  America,  where  the  conveniences  for  repairing  or 
replacing  parts  are  not  close  at  hand. 

Erection  requirements  or  other  special  conditions  at  a  site  often  affect 
materially  the  relative  economics  of  the  various  types  of  movable  spans — 
sometimes  to  such  an  extent  as  to  outweigh  all  other  considerations. 
They  may  affect  either  favorably  or  unfavorably  any  of  the  different 
types.  Any  given  site  should,  therefore,  receive  special  study  from  this 
viewpoint. 

Economics  of  Swing  Spans 

Although  the  author  does  not  believe  that  there  is  to-day  any  necessity 
for  this  type  of  structure  nor  any  advantage  to  be  derived  from  building 
one;  yet,  as  all  engineers  may  not  agree  with  him,  it  will  be  well,  in  order 
that  this  chapter  may  not  be  lacking  in  completeness,  to  give  a  short  disser- 
tation concerning  the  economics  of  some  of  the  different  types  of  swing 
in  common  use. 

Rim-Bearing  versus  Center-Bearing  Spans 

The  choice  between  these  two  types  is  mainly  a  matter  of  taste  or 
sometimes  one  of  prejudice;  for  there  is  no  great  difference  in  their  first 
costs,  what  there  is  being  in  favor  of  the  latter,  which  also  has  a  slight 
advantage  in  respect  to  amount  of  power  required  to  operate.  In  the 
author's  opinion,  the  principal  economic  advantage  of  the  center-bearing 
type  is  due  to  the  smaller  diameter  of  the  pivot  pier. 

There  is  a  difference  of  opinion  amongst  railroad  engineers,  and  even 
amongst  high  authorities  on  bridges,  concerning  both  the  relative  merits 
and  the  economics  of  these  two  types.  The  late  C.  C.  Schneider,  Past 
President  of  the  American  Society  of  Civil  Engineers,  said:  "The  center- 
bearing  type,  designed  in  accordance  with  good  modern  practice,  offers 
more  advantages  than  the  rim-bearing  type,  and  should  always  receive 
the  first  consideration  in  determining  upon  a  design.  It  requires  less  power 
to  turn,  has  a  smaller  number  of  moving  parts,  is  less  expensive  to  con- 
struct and  maintain,  involves  less  accurate  construction  than  the  rim- 
bearing  bridge,  and  does  not  as  easily  get  out  of  order.  The  structural 
and  the  operating-machinery  parts  are  entirely  separate;  and  when  the 
bridge  is  closed,  it  forms  either  two  independent  fixed  spans,  or  a  fixed  span, 
continuous   over   two   openings,   resting   on   firm,    substantial  supports. 


288  '  ECONOMICS   OF   BRIDGEWORK  Chapter  XXX 

There  are  no  ambiguities  in  the  calculations  in  reference  to  the  distribution 
of  the  load;  and  the  distance  required  from  base  of  rail  to  masonry  is 
generally  less  than  that  required  for  a  rim-bearing  bridge  with  proper  dis- 
tribution of  the  load  over  the  drum.  Any  irregular  settlement  of  the 
masonry  does  not  materiall}'  affect  its  operation. 

"  On  the  other  hand,  the  rim-bearing  bridge  requires  a  circular  girder 
or  drum  of  difficult  and  expensive  construction,  a  ring  of  accurately- 
turned  rollers,  and  circular  tracks  that  necessitate  great  care  in  their  con- 
struction and  delicate  adjustment  in  their  erection,  in  order  to  make  the 
bridge  operate  satisfactorily.  Repairs  are  troublesome  and  expensive; 
and  any  irregular  settlement  of  the  masonry  will  throw  the  whole  turn- 
ing apparatus  out  of  order." 

As  an  illustration  of  diametrically  opposite  opinion,  the  following 
quotation  from  a  printed  statement  by  the  late  C.  H.  Cartlidge,  formerly 
Bridge  Engineer  of  the  Chicago,  Burlington,  and  Quincy  Railwaj-,  is 
directly  to  the  point.  "The  writer's  experience  with  center-bearing 
draw-spans  has  been  such  as  to  prejudice  him  against  them  for  spans  of 
any  magnitude.  It  seems  difficult  at  any  reasonable  cost  to  proportion 
the  pivot-bearing  so  that  it  will  not  wear;  and  any  wear  on  a  pivot-bearing 
is  expensive  to  repair.  On  one  draw  the  wearing  away  of  the  bronze  bear- 
ing in  the  pivot  allowed  the  upper  and  lower  castings  to  rub,  making  the 
turning  of  the  draw  a  very  noisy  operation,  while  the  few  wheels  provided 
to  steady  the  span  during  turning  were  overworked  and  cut  the  circular 
track  badly." 

There  is  a  combination  of  the  rim-bearing  and  the  center-bearing 
swings  advocated  by  some  engineers ;  but  the  author,  on  general  principles, 
objects  to  hybrid  designs,  and  especially  in  this  case  where  there  must 
exist  a  great  uncertainty  concerning  the  distribution  of  load  between  rim 
and  pivot. 

Bob-Tailed  Swing  versus  Ordinary  Siving 

While  there  is  apparently  a  saving  in  first  cost  by  cutting  down  the 
length  of  one  arm  of  a  swing-span  so  as  to  convert  it  into  a  "bob-tailed" 
structure,  that  saving  is  generally  absorbed  by  the  adoption  of  more 
power  and  heavier  machinery  (with  which  to  operate  against  unbalanced 
wind  loads),  heavy  counterweights,  and  the  special  metal  needed  to  support 
the  said  counterweights. 

There  are  other  questions  of  economics  in  swing  spans,  such  as  plate- 
girder  versus  truss-span  structures,  and  continuous  versus  non-continuous 
trusses  over  pivot  piers;  but  in  view  of  the  fact  that  the  author  is  opposed 
on  principle  to  building  any  more  swing  spans,  it  were  useless  to  carry 
further  this  economic  dissertation,  especially  as  the  subject  of  swing  bridges 
is  treated ^luitc  thoroughly  in  Chapter  XXIX  of  "Bridge  Engineering." 


ECONOMICS    OF   MOVABLE    SPANS  289 

Economics  of  Bascule  Spans 

Bascule  spans  may  be  divided  into  two  general  classes — single-leaf  and 
double-leaf.  The  former  type  is  superior  to  the  latter  in  rigidity  but 
inferior  in  appearance,  because  of  lack  of  symmetry.  In  the  opinion  of 
most  railway  engineers,  on  account  of  the  difficulty  in  properly  connecting 
the  outer  ends  of  the  two  leaves,  the  double-leaf  bascule  ought  not  to  be 
employed  for  steam-railway  bridges,  for  the  reason  that  the  lack  of  rigidity 
and  the  great  deflection  involved  are  not  compatible  with  truly-first-class 
construction. 

There  is  an  economic  question  in  connection  with  bascules  that  is  very 
difficult  to  solve,  viz.,  what  is  the  distance  between  centers  of  bearings  at 
which  it  will  save  in  first  cost  to  change  from  a  single-leaf  to  a  double-leaf 
structure?  In  the  case  of  a  bridge  in  which  the  counterweights,  the 
machinery,  and  their  supporting  metal  are  below  the  deck,  the  economic 
limit  for  the  single-leaf  span  will  almost  always  be  less  than  it  is  when 
those  parts  of  the  structure  are  above;  and,  in  the  former,  the  closer  the 
deck  is  to  high-water  level,  the  shorter  will  be  this  limiting  economic  dis- 
tance. The  reason  for  this  is  that,  with  a  single-leaf  structure  and  a  small 
vertical  distance  between  grade  and  high  water,  unless  the  moving  span 
be  short,  either  the  counterweight  will  be  excessively  heavy,  or  else  a  pit 
will  have  to  be  provided  to  receive  the  tail  end.  The  adoption  of  either 
of  these  expedients  causes  the  cost  of  structure  to  rise  rapidly. 

One  of  the  reasons  why  the  cost  of  a  two-leaf  bascule  tends  to  exceed 
that  of  the  corresponding  one-leaf  structure  is  that  in  the  former  there 
must  be  a  holding-down  reaction  at  each  end;  and  because  that  reaction 
involves  the  use  of  considerable  extra  metal  in  the  flanking  spans  or  over 
the  piers — much  of  it  being  high  priced.  Since  this  anchorage  is  required 
for  live  load  only,  it  follows  that  the  condition  of  small  live  load  and 
large  dead  load  favors  the  double-leaf  bascule,  whereas  that  of  large  live 
load  and  small  dead  load  favors  the  single-leaf  type. 

With  counterweights,  towers,  and  machinery  above  the  deck,  the 
clear  opening  for  equal  cost  of  one-leaf  and  two-leaf  spans  is  probably  so 
great  as  to  exceed  the  length  above  which  it  becomes  economic  to  pass 
from  bascule  to  vertical  lift.  While  the  author  has  made  no  special 
figures  to  estabHsh  beyond  all  doubt  the  correctness  of  this  statement, 
his  experience  with  bascule  designing  warrants  him  in  drawing  the  con- 
clusion. He  is  of  the  opinion  that,  for  the  overhead-counterweight  type, 
the  length  for  equal  cost  lies  between  one  hundred  and  fifty  and  two 
hundred  feet;  and,  for  such  a  span-length,  the  vertical  Hft,  for 
the  sake  of  economy,  if  for  no  other  reason,  should  supplant  the 
bascule. 

It  is  also  the  author's  opinion,  based  on  practical  experience  rather 
than  upon  extensive  special  economic  computations,  that  the  double-leaf 
type  of  bascule  is  necessitated  only  by  reason  of  aesthetics  or  because  of  a 


290  ECONOMICS   OF   BRIDGEWORK  Cil\pter  XXX 

too  limited  vertical  distance  between  the  elevations  of  grade  and  high 
water. 

The  simplest  foim  of  bascule  is  the  ordinaiy  heel-comiterbalaneed, 
trunnion  type;  and  this  is  the  kind  which  is  generally  adopted  when  the 
minimum  clearance  allowed  above  water  will  permit.  In  manj^  cases  the 
height  is  not  sufficient  for  the  heel  of  the  span  and  the  counterweight  to 
clear  the  water  or  the  pier-tops,  and  then  the  span  must  be  lengthened 
and  a  water-tight  pit  must  be  provided  into  which  the  said  heel  and  the 
counterweight  may  descend.  The  expense  of  construction  thus  involved 
is  very  great;  and,  consequently,  the  more  comphcated  and  unsightly 
types,  having  towers  and  counterweights  above  the  roadway,  are  re- 
sorted to. 

Sometunes  cases  occur  in  which  the  height  above  water  is  insufficient 
for  a  simple,  heel-balanced  bridge  of  the  orcUnaiy  type  without  water- 
tight pits,  and  where  the  adoption  of  unsightly  towers  and  counterweights 
is  barred  for  aesthetic  reasons.  Again,  in  the  usual  heel-counterbalanced 
trunnion  structures,  it  is  obKgatory  so  to  dispose  the  counterweighting 
that  the  center  of  gravity  of  the  entire  moving  mass  shall  he  upon  the  axis 
of  rotation;  and  this  generally  necessitates  the  location  of  a  considerable 
portion  of  the  counterweight  above  the  deck,  to  the  detrmient  of  the 
appearance  of  the  bridge.  Under  such  conditions  it  is  necessary  to  provide 
a  heel-balanced,  trunnion  structure,  in  which  the  coincidence  of  the  center 
of  gravity  and  the  axis  of  rotation  are  not  obhgatory,  and  by  which  the 
employment  of  either  pits  or  unsightly  towers  is  avoided. 

These  desiderata  can  be  accomplished  by  a  partial  balance  of  span- 
weight,  completing  the  said  balance  by  means  of  a  counterweight  sup- 
ported on  a  beam  pivotally  connected  at  one  end  to  the  heel,  and  sup- 
ported at  its  other  end  by  a  roller  or  truck  which  passes  forward  and  back- 
ward on  a  track  when  the  span  opens  or  closes,  according  to  a  series  of 
patents  lately  taken  out  by  Mr.  Thomas  EUis  Brown,  Jr. 

Either  of  the  two  primary  types  of  bascule  may  be  divided  into  three 
general  classes,  viz.,  trunnion,  rolling-hft,  and  roller-bearing.  All  of 
these  are  good,  but  none  is  best  for  all  conditions,  nor  can  it  be  said  abso- 
lutely that  one  is  always  more  economical  than  another.  Each  has  its 
good  points  and  each  its  bad  ones;  and  some  are  fitted  for  one  location  and 
not  for  another. 

The  rolling-hft  is  sometimes  the  cheapest,  as  has  been  shown  often  by . 
competitive  bids  on  different  types  submitted  by  Contractors;  but  it  is 
not  good  practice  to  adopt  it  when  the  pier  foundations  are  of  piling,  on 
account  of  the  shifting  of  the  center  of  gravity  of  the  load  on  the  piles  as 
the  span  rolls  backward  and  forward,  and  because  of  the  possibihty  of  pier 
settlement.  The  extension  and  compression  of  the  outer  piles,  caused  by 
such  shifting,  has  a  tendency  to  crack  the  superimposed  masonry.  The 
great  advantage  of  this  type  is  its  retreating  bodily  out  of  the  way  of 
passing  vessels. 


ECONOMICS   OF   MOVABLE    SPANS  291 

The  Trunnion  type  is  comparatively  simple,  but  has  not  the  advantage 
of  the  retreating  span  possessed  by  the  rolKng  lift,  and  hence  often  neces- 
sitates a  rather  long  leaf  for  a  fixed  clear  opening. 

By  the  adoption  of  the  Waddell  and  Hariington  detail  for  bearings, 
the  ambiguity  of  stress  distribution  and  the  secondary  stresses,  involved 
through  the  bending  of  the  ordinary  trunnion-axle  or  trunnion-girder, 
are  entirely  avoided,  thus  rendering  the  design  of  structure  decidedly 
more  scientific  and  cutting  out  some  abnormally  high  intensities  of  working 
stresses. 

The  roller-bearing  type  has  not  been  much  used.  Wlien  properly 
designed,  it  is  neat,  scientific,  and  in  every  essential  way  excellent,  but  is 
not  pre-eminently  economic. 

There  is  considerable  rivalry  between  the  patentees  of  the  various 
standard  types  of  bascule.  Each  one  seems  convinced  not  only  of  the 
superiority  of  his  own  type  but  also  of  its  greater  economy;  consequently 
it  is  not  an  easy  matter  to  draw  conclusions  on  bascule  economics  that  will 
satisfy  all  concerned.  This  much,  however,  can  be  said — when  the  bas- 
cule is  entirely  a  deck  structure,  the  most  economic  type  will  depend 
greatly  upon  the  governing  conditions;  but  when  the  counterweights, 
towers,  machinery,  etc.,  are  above  the  deck,  the  Strauss  and  the  Brown 
types  appear  to  have  an  advantage  over  all  the  others.  Until  a  short  time 
ago  the  Strauss  heel-trunnion  type  held  the  record  for  economy,  but  the 
lately-developed  Brown  Balance-Beam  type  appears  to  be  slightly  more 
economical  than  any  other  bascule  in  the  overhead-counter-weight  class. 
At  present  there  is  no  example  of  this  new  bascule  in  existence,  and  the 
only  one  yet  designed  in  detail  is  that  for  a  proposed  crossing  of  the  Mystic 
River  at  Mystic,  Conn.  This  was  designed  by  the  firm  of  Thos.  E.  Brown 
and  Son,  Consulting  Engineers.  Estimates  of  quantities  of  materials 
made  from  their  finished  drawings  indicate  that  the  Browns  have  suc- 
ceeded in  producing  the  most  economic  bascule  with  overhead  counter- 
weight yet  evolved. 

Economics  of  Vertical-Lift  Spans 

The  governing  conditions  which  prove  economic  for  the  vertical  lift, 
in  comparison  with  the  other  types  of  movable  span,  are  as  follows : 
First.     Low  vertical  clearance. 
Second.     Large  horizontal  clearance. 
Third.     Heavy  moving  span. 
Fourth.     Existence  of  fairly-long  flanking-spans. 

Fifth.     Deep  foundations,  especially  when  the  flanking-spans  are  long. 
Sixth.     Expensive  piers,  when  flanking-spans  are  long. 
Seventh.     Skewed  crossings. 
Eighth.     Concrete  deck  desired. 
Ninth.     Other  first-class  deck,  especially  if  heavy. 


292  ECONOMICS   OF  BRIDGEWORK  Chapter  XXX 

Tenth.     Shifting  channel. 

Eleventh.     High  wind  pressures  to  be  provided  for. 

Twelfth.     Wide  deck. 

Thirteenth.     Necessity  for  quick  operation. 

A  low  vertical  clearance  is  evidently  favorable  to  the  vertical  lift.  The 
real  factor  in  this  case  is  the  required  vertical  movement  of  the  hft  span. 
A  greater  clearance  above  the  water  when  the  span  is  down  favors  the 
vertical  hft;  smce,  for  any  required  clear  height  with  the  span  raised,  the 
vertical  movement  is  reduced. 

A  large  horizontal  clearance  favors  the  vertical  hft  in  comparison  with 
the  bascule.  For  a  given  weight  of  moving  span,  the  towers,  counter- 
weights, and  machinery  cf  a  vertical-lift  bridge  are  independent  of  the 
span-length,  while  those  items  for  a  bascule  vary  nearly  directly  therewith. 

As  will  be  explained  fully  later  on  in  this  chapter,  the  ratio  of  vertical 
and  horizontal  clearances  for  equal  costs  of  bascules  and  vertical  lifts  is 
generally  about  unity,  being  somewhat  less  for  short  and  hght  spans,  and 
materially  greater  for  long  and  heavy  ones. 

Increased  weight  of  span  is  favorable  to  the  vertical  hft.  This  is 
chiefly  due  to  the  weight  of  the  rear  legs  and  bracing  of  the  towers,  which, 
for  a  given  height  thereof,  are  Dearly  as  heavy  for  hght  spans  as  for  heavy 
ones.  For  a  very  hght  span  and  high  vertical  clearance,  the  weight  of  the 
towers  may  nearly  equal  that  of  the  span;  whereas,  for  a  heavy  span  and 
the  same  vertical  clearance,  it  may  be  only  one-third  of  the  said  weight. 
There  is  no  such  variatioD  in  the  case  of  the  bascule,  since  the  weight  of  the 
bracing  is  a  smaller  proportion  of  the  total  weight  of  the  towers  and  coun- 
terweight trusses. 

A  layout  in  which  the  economic  length  of  the  flanking-spans  is  much 
greater  than  the  proper  length  of  a  bascule  tower-span  favors  the  vertical 
lift.  In  such  a  case  the  rear  legs  of  the  vertical-lift  towers  rest  on  the 
flanking-spans  without  producing  any  material  stresses  therein.  But  in 
bascules  with  overhead  counterweights  it  will  be  necessary  to  put  in  an 
additional  pier,  or  to  carry  the  weight  of  the  counterweight  on  one  of  the 
flanking-spans,  or  to  put  the  counterweight  trunnion  over  the  pier  and 
cantilever  the  flanking-span  out  to  support  the  trunnions  of  the  moving 
span.  The  first  method  is  most  economic  where  the  substructure  is 
cheap,  and  the  third  generally  where  the  substructure  is  expensive.  The 
third  scheme  requires  ample  fenders  to  protect  the  cantilevered  portions 
from  passing  vessels.  In  deep  water  these  fenders  may  be  impracticable 
or  very  costly,  thus  making  the  second  arrangement  the  best. 

Over  a  canal,  or  a  small  canalized  river,  the  layout  often  calls  for  a 
movable  span  and  two  short  approach  spans.  In  such  a  case  four  piers 
will  be  required  for  either  the  bascule  or  the  vertical  lift.  This  case  is 
nearly  always  less  favorable  to  the  vertical  lift  than  the  layout  where  long 
flanking-spans  are  called  for. 

Deep  foundations  and  expensive  pic^s  are  favorable  to  tlie  vertical  lift, 


ECONOMICS    OF   MOVABLE    SPANS  293 

as  compared  with  the  bascule,  when  long  flanking-spans  are  employed; 
but  for  crossings  over  canals  or  canalized  rivers  the  cost  of  the  substructure 
usually  has  little  effect  on  the  comparison.  A  crossing  where  the  piers 
rest  on  piles  or  sand  is  especially  favorable  to  the  vertical  lift,  since  the 
total  loads  for  that  type  are  less  than  those  for  the  bascule.  Rolling-lift 
bascules  are  not  well  adapted  to  such  foundations.  Deep  foundations  are 
usually  unfavorable  bo  the  swing,  on  account  of  the  large  base  of  the  pivot 
pier. 

Advantage  can  be  taken  of  a  badly-skewed  crossing  by  the  vertical 
lift;  for  both  the  span  and  the  towers  may  be  skewed  with  very  little 
extra  expense,  while  at  least  one  end  of  the  bascule  will  have  to  be  squared, 
thus  lengthening  the  span  and  increasing  the  cost.  It  is  true  that  a  sim- 
ilar advantage  can  be  taken  with  the  swmg  by  making  both  ends  skewed, 
but  that  would  prevent  the  reversing  of  ends.  However,  there  is  not 
often  any  real  necessity  for  such  reversal. 

A  channel  that  has  a  tendency  to  shift  will  give  the  vertical  lift  a  great 
advantage  over  either  of  the  competing  types,  because  it  is  the  only  one 
of  the  three  which  permits  a  change  in  the  location  of  the  opening  span 
without  necessitating  excessive  expense. 

A  requirement  for  high  wind  pressure  militates  greatly  against  the  bas- 
cule, because  it  involves  an  augmenting  of  the  power  and,  consequently, 
also  the  cost  of  the  operating  machinery;  but  it  affects  hardly  at  all  the 
cost  of  either  the  vertical  lift  or  the  swing. 

In  a  modern,  first-class  structure,  where  a  concrete  deck  should  be  used 
to  ehminate  fire  risk,  the  vertical  lift  and  the  swing  can  be  employed; 
but  the  bascule  cannot,  if  there  is  to  be  paving  on  the  concrete.  While  a 
concrete  deck  without  other  paving  could  be  used  on  a  bascule,  the  span 
would  be  so  heavy  that  a  vertical-hft  bridge  would  always  be  the  cheaper, 
except  for  a  very  high  lift  with  a  short  span. 

The  use  of  a  block  pavement  or  other  heavy  type  of  deck  favors  a 
vertical  lift  as  compared  with  the  bascule,  since,  for  the  latter,  extra  expense 
is  required  properly  to  fasten  the  blocks  so  that  they  shall  not  fall  off. 
Furthermore,  the  greater  weight  of  the  deck  favors  the  vertical  lift. 

The  widening  of  the  deck  lengthens  the  moving  span  in  any  swing, 
and  increases  the  size  of  the  pivot  pier  and  the  cost  of  the  pier  protection. 
In  a  skewed  crossing  it  augments  the  length  of  a  bascule.  Since  a  wider 
deck  involves  a  heavier  structure,  this  factor  also  favors  the  vertical  lift. 

In  respect  to  quickness  of  operation,  this  condition  does  not  affect 
materially  the  comparative  economics  of  vertical  lifts  and  single-leaf  bas- 
cules; but  both  the  double-leaf  bascule  and  the  swing  are  at  a  disad- 
vantage, since  they  take  fully  twice  as  long  to  operate  as  do  the  other  types. 

The  question  of  flanking  spans  is  of  such  importance  that  the  author 
has  found  it  necessary  in  his  practice  and  in  his  economic  studies  to  divide 
the  vertical-lift  bridge  into  two  distinct  types — one  where  there  are  fixed 
spans  flanking  the  movable  span,  and  the  other  where  there  are  not. 


294  ECONOMICS   OF  BRIDGEWORK  Chapter  XXX 

With  regard  to  the  towers,  the  vertical  hfts  may  be  divided  into  three 
classes,  viz., 

A.  Structures  with  towers  having  inclined  rear  legs. 

B.  Structures  with  towers  having  vertical  rear  legs. 

C.  Structures  having  towers,  each  composed  of  a  single  bent,  and  gen- 
erally, but  not  necessarily,  connected  at  their  tops  by  a  span  or  strut  cross- 
ing the  opening. 

In  respect  to  the  economics  of  these  three  classes,  it  may  be  stated  that, 
for  a  combination  of  a  short  span  and  a  moderate  vertical  clearance.  Class  C 
is  the  most  economic;  but  it  is  not  compatible  with  rigid  construction  for 
high  clearances — also  that  Class  A  is  always  more  economic  than  Class  B, 
because  the  latter  involves  the  doubling  of  the  nmnber  of  sheaves  and  a 
considerable  increase  in  the  weight  of  the  towers,  as  well  as  a  small  extra 
amount  of  wire  rope.  It  is  found  advantageous,  however,  in  the  case  of 
very-badly-skewed  structures,  because  it  throws  the  large  and  clumsy 
counterweights  entirely  outside  of  the  towers  and  permits  of  a  thorough 
system  of  internal  sway  bracing  for  the  latter. 

Economics  in  Detailing  of  Vertical  Lifts 

There  are  a  few  economic  problems  that  arise  in  the  detailing  of  ver- 
tical-hft  bridges,  the  principal  of  which  are  the  kinds  of  materials  for 
counterweights,  the  use  or  non-use  of  counterbalancing  chains,  the  employ- 
ment or  omission  of  buffers  and  the  best  type  of  same,  the  character  of 
pavement  base,  the  location  of  the  machinery  house,  and  the  determina- 
tion of  the  number  and  the  size  of  the  supporting  ropes  which  will  make 
the  combined  cost  of  ropes  and  sheaves  a  minimum. 

In  respect  to  the  cheapest  material  for  counterweights,  in  most  cases  it  is 
ordinary  concrete;  but  sometimes,  when  the  space  is  limited,  it  pays  to 
make  the  mass  heavier  by  incorporating  in  it  materials  of  greater  density 
than  that  of  ordinary  stone,  such  as  iron  ore  or  pig  iron.  The  latter  was 
employed  entirely  for  the  counterweights  of  the  Halsted-Street  Lift- 
Bridge,  the  first  structure  of  the  type  on  a  large  scale  ever  built;  but 
its  utilization  was  not  economic,  consequently  in  subsequent  structures 
its  employment  was  abandoned. 

As  to  whether  it  is  advisable  to  use  chains  for  the  purpose  of  keeping 
the  main  cables  always  counterbalanced,  that  is  an  economic  problem 
which  is  dependent  upon  the  kind  of  power  used,  how  often  the  bridge 
is  to  be  operated,  and  the  extent  of  the  span  movement.  They  should 
not  be  employed  for  low  lifts,  as  in  these  the  unbalanced  rope-load  is  just 
about  right  to  hold  down  the  span  properly.  The  author  favors  the 
adoption  of  such  chains  for  most  cases  where  the  vertical  movement  is 
large,  so  as  to  make  the  peak  load  of  power  a  minimum  and  thus  keep 
down  the  cost  of  both  installation  and  operation;  but  he  recognizes  that, 
when  the  price  of  power  is  low  and  the  bridge  is  not  to  be  openetl  often,  it 


ECONOMICS   or  MOVABLE   SPANS  295 

it  would  be  economical  to  omit  the  said  chains.  These  can  be  made  of 
cast-iron  links  bored  for  small  pins,  so  as  to  keep  their  pound  price  as  low 
as  possible. 

It  may  be  all  right  to  omit  the  buffers  entirely  and  trust  to  the  auto- 
matic brakes  to  stop  the  span,  but  the  author  prefers  to  adopt  the  addi- 
tional precaution  of  using  the  buffers  as  a  safeguard,  in  case  that  anything 
should  go  wrong  with  the  operation  of  the  brakes.  He  has  tried  two  kinds 
of  buffers,  viz.,  oil  and  air,  and  prefers  the  latter  on  account  of  greater 
reliability  and  cleanliness. 

In  respect  to  the  character  of  base  for  pavement,  it  will  generally  be 
economical  to  use  the  hghtest  practicable,  consistent  with  proper  require- 
ments for  strength  and  stiffness.  The  modern,  stiffened-buckle-plate  floor 
with  a  thin  layer  of  concrete  thereon  supporting  three-inch  wooden  blocks, 
described  in  Chapter  XXI,  will  save  the  lifting  of  considerable  weight; 
and  the  consequent  reduction  in  cost  of  ropes,  sheaves,  counterweights,  and 
capitalized  power  will  generally  more  than  offset  the  extra  cost  of  the  lighter 
base. 

From  motives  of  economy  alone,  it  is  better  to  place  the  machinery 
house  in  one  of  the  towers  instead  of  on  the  span;  because  it  takes  extra 
truss-metal  to  carry  it  in  the  latter  place,  and  this  extra  metal  and  the 
weight  of  the  house  with  its  machinery  augment  the  cost  of  ropes,  sheaves, 
counterweights,  and  power.  But  generally  the  operator  obtains  a  much 
better  view  of  passing  vessels  fronq.  the  middle  of  the  span  than  he  could 
from  the  tower  or  anywhere  else,  consequently  it  will  then  be  better  to  put 
the  house  on  the  span  in  spite  of  the  extra  expense  involved  by  so  doing. 

Finally,  in  respect  to  the  determination  of  number  and  sizes  of  sup- 
porting cables,  it  may  be  stated  that  the  greater  the  number  of  cables 
the  smaller  their  diameter  and  the  smaller  the  legitimate  diameter  of  the 
sheaves;  but  the  greater  the  number  of  ropes  the  wider  the  said  sheaves. 
Again,  multiplicity  of  ropes  means  a  multiplicity  of  expensive  details 
for  their  connection;  hence  the  determination  of  main-rope  diameter  is  a 
question  that  generally  has  to  be  solved  by  good  engineering  judgment 
based  upon  experience  rather  than  by  economics  pure  and  simple.  The 
author's  usual  practice  is  to  adopt  four  ropes  per  corner  for  loads  up  to 
250,000  lbs.,  eight  from  250,000  to  1,250,000  lbs.,  and  sixteen  for  greater 
loads. 

There  is  a  combination  of  vertical  lift  and  cantilevers  that  has  lately 
proved  to  be  economic.  The  author  evolved  it  many  years  ago,  but  did 
not  publish  anything  concerning  it,  preferring  to  await  the  psychological 
moment  for  utilizing  it.  The  opportunity  did  not  present  itself  until 
1918,  when,  as  a  member  of  the  Board  of  Advisory  Engineers  to  the 
Public  Belt  Railroad  Commission  of  New  Orleans,  he  prepared  a  low-level- 
bridge  layout  with  a  verticai-lift  span  for  a  proposed  crossing  of  the  Miss- 
issippi River  near  that  city.  He  had  adopted  for  the  movable  span  a 
clear  opening  of  three  hundred  feet;  and,  when  trying  to  obtain  an  informal 


296  ECONOMICS   or  BRIDGEWORK  Chapter  XXX 

approval  of  that  length  by  the  then  Chief  of  Engineers  of  the  United  States 
Army,  he  was  told  that,  in  view  of  the  possibihty  of  the  Mississippi  being 
navigated  in  the  future  by  large  flotillas  of  barges,  the  suggested  opening 
would  be  too  small.  Thereupon  he  made  another  layout  having  the  same 
length  of  vertical-lift  span  but  aclear  width  between  piers  of  five  hundred 
feet,  supporting  the  towers  on  the  cantilevered  ends  of  the  two  flanking- 
spans.  This  arrangement  would  permit  of  the  flotilla  steamer  passing 
through  the  opening  beneath  the  raised  lift-span  and  of  the  barges  slipping 
under  the  cantilever  arms,  in  case  that  the  current  should  swing  the  flotilla 
broadside  to  the  structure,  the  said  cantilever  arms  having  sufficient  ver- 
tical clearance  above  extreme  high  water  to  permit  such  paLsage  under 
any  river  condition.  When  the  author  submitted  this  new  layout  to  the 
local  U.  S.  Engineer  officer  in  charge  at  New  Orleans,  the  request  was 
made  for  ah  economic  investigation  of  the  structure  with  not  only  the  sug- 
gested clear  openings  of  300  and  500  feet,  but  also  with  those  of  600  and 
700  feet,  adopting  a  lift  span  of  350  feet  for  the  600-ft.  opening  and  a 
400-ft.  one  for  the  700-ft.  opening.  The  result  of  the  investigation  showed 
that  the  500-ft.  opening  was  more  economic  than  the  300-ft.  one,  that  the 
latter  made  the  total  cost  of  structure  about  the  same  as  did  the  600-ft. 
opening,  but  that  the  700-ft.  opening  was  so  decidedly  uneconomic  as 
practically  to  be  prohibitive. 

Early  in  1920  the  author's  Indian  agents  in  Calcutta  wrote  asking  him 
whether  he  could  evolve  a  design  for  crossing  the  Hoogly  River  at  their  city 
by  a  single  span  in  a  manner  that  would  comply  satisfactorily  with  certain 
unusual  and  extremely  drastic  physical  conditions.  These  conditions 
were  met  by  the  utilization  of  the  above-mentioned  scheme  of  a  vertical 
lift  and  cantilever  arms,  combined  with  pier  foundations  of  built-up  piles 
of  exceedingly  great  length  sunk  by  jetting.  This  type  of  piling  was  orig- 
inated by  the  author  so  many  years  ago  that  he  had  actually  forgotten 
about  the  matter  and  had  to  resurrect  the  drawings  from  an  ancient  office- 
file.  The  layout  suggested  is  shown  in  Fig.  30a.  As  can  be  seen  by 
inspection,  it  contains  still  another  economic  innovation,  viz.,  the  support- 
ing of  the  counterweights,  which  balance  the  weight  of  the  moving  span, 
from  the  tops  of  the  columns  over  the  main  piers,  thus  relieving  both  the 
cantilever  arms  and  the  anchor  arms  from  stresses  due  to  the  said  counter- 
weights. There  were  some  other  economic  innovations  involved  in  the 
study  and  estimate  that  are  not  shown  on  the  layout;  but  it  is  not  neces- 
sary to  discuss  them  here. 

An  alternative  design  was  submitted  at  the  same  time  to  the  agents 
mentioned  by  substituting  a  double-leaf  bascule  for  the  vertical-lift  span, 
with  the  statement,  however,  that  the  first-described  layout  is  in  every 
way  preferable,  excepting  only  for  the  fact  that  the  bascule  design  gives  an 
unlimited  vertical  cleai-ance.  The  Brown  wire-rope  type  of  bascule  was 
used;  and  the  counterweights  were  placed  over  the  main  piers,  as  in  the 
vertical-lift  design. 


Fio.  30a.    Layout  for  ]*roposed  Hoogly  lliver  Bridge  at  Calcutta,  India. 


ECONOMICS   OF   MOVABLE    SPANS  297 

Unfortunately,  the  "Powers"  at  Calcutt?,  have  not  yet  seen  fit  to  give 
these  layouts  consideration;  and  it  seems  probable  that  the  time  and 
gray  matter  expended  by  the  author  in  evolving  this  solution  of  a  knotty 
and  interesting  problem  will  be  wasted — at  least  from  a  pecuniary  point  of 
view — hence,  in  order  that  such  waste  may  not  be  total  and  permanent, 
he  is  now  presenting  to  the  engineering  profession  the  results  of  this 
economic  study. 

Comparative  Costs  of  Various  Types  of  Movable  Spans 

The  collection  of  the  necessary  data  concerning  the  quantities  of  mate- 
rials in  movable  spans  has  been  no  easy  task,  because  the  designers  and 
builders  of  such  structures  seldom  publish  the  total  weights  of  metal 
involved,  nor,  what  is  equally  important,  the  division  of  the  said  weights 
into  various  logical  groups,  such  as  moving  span,  towers,  counterweight 
trusses,  etc.  Furthermore,  such  records  as  can  be  collected  need  to  be 
carefully  plotted  and  compared  on  some  logical  basis,  since  different 
bridges  are  designed  for  various  specifications  and  often  under  dissimilar 
conditions. 

The  analyses  of  all  these  weights  have  been  prepared  for  this  economic 
investigation  by  the  author's  assistant  engineer,  Mr.  Shortridge  Hardesty. 
Comparisons  have  been  made  with  great  thoroughness  between  vertical- 
lift  bridges  and  both  the  heel-trunnion  and  the  Brown  balance-beam, 
single-leaf  bascules;  firstly,  because  it  was  possible  to  secure  the  fullest 
data  concerning  these  types;  secondly,  because,  for  many  layouts,  the 
logical  choice  would  be  one  of  them;  and,  thirdly,  because  it  is  a  compara- 
tively simple  matter  to  contrast  them  fairly  and  definitely.  Swing  spans 
and  deck  bascules  with  underneath  counterweights  have  also  been  investi- 
gated, but  questions  of  types  of  piers,  distance  from  grade  to  water  line, 
aesthetic  considerations,  and  other  factors  affect  the  comparisons  so  largely 
as  to  make  the  results  considerably  influenced  by  the  personal  equation  of 
the  designer  and  by  the  conditions  of  each  individual  case.  Railway 
bridges  have  been  used  as  a  basis  for  the  most  part,  because  the  best  records 
available  deal  with  that  class  of  structure,  and  because  there  is  less  variation 
in  them  than  in  highway  bridges. 

For  the  vertical-lift  bridge  the  author  had  at  hand  the  records  of  some 
thirty  cases  designed  in  his  office,  supplemented  by  complete  curves 
of  weights  of  towers  for  different  heights  thereof  and  for  various  weights 
of  moving  spans.  The  weights  of  the  different  machinery  groups,  such  as 
ropes,  sheaves,  equalizers,  operating  machinery,  etc.,  were  plotted  in  terms 
of  the  weight  of  the  moving  span  and  the  height  of  lift.  Curves  of  average 
weights  were  then  drawn  for  each  group.  The  same  was  done  for  each  of 
the  items  of  structural  metal.  These  various  curves,  after  being  first 
drawn  in  terms  of  the  weight  of  the  moving  span,  were  replotted  in  terms  of 
the  weight  of  a  fixed  span  of  the  same  length  and  carrying  capacity. 


298  ECONOMICS   OF   BRIDGEWORK  Cila^pter  XXX 

vertical-lift  span  with  the  machinery  and  motors  in  a  house  at  the  center  of 
the  span  weighs  over  ten  per  cent  more  than  the  corresponding  fixed  span. 

For  the  railway,  heel-trunnion  bascule  there  were  available  complete 
detailed  weight-records  of  seven  bridges,  complete  detailed  estimates  for 
several  more  prepared  by  their  designers,  and  summarized  estimates  for 
about  a  dozen  others.  Most  of  them  were  for  double-track-railway 
bridges.  The  percentages  of  the  weights  of  the  towers  (less  the  tower  floor- 
systems),  the  counterweight  trusses  and  girders,  the  links,  the  operating 
struts,  etc.,  in  terms  of  the  weights  of  the  moving  span  were  then  figured, 
the  machinery  girders  being  included  with  these  items  regardless  of  whether 
the  motors  were  on  the  span  or  in  the  tower.  The  percentages  were  then 
computed  in  terms  of  the  weight  of  the  corresponding  fixed  span,  the 
bascule  leaf  being  a  few  per  cent  heavier  than  the  said  span.  These  latter 
percentages  were  then  plotted  with  the  lengths  of  moving  spans  as  abscisses. 
These  plots  provided  a  sufficicmt  number  of  points  for  the  drawing  of  fair 
average  curves  for  double-track  bridges.  The  weights  of  trunnions,  pins, 
and  machinery,  in  percentages  of  the  weights  of  the  corresponding  fixed 
spans,  were  then  plotted,  and  an  average  curve  was  drawn. 

Fig.  306  gives  the  resulting  curves  for  both  bascules  and  vertical  lifts. 
The  full  hues  for  the  tower  an' I  counterweight  steel  of  the  vertical  lift  apply 
when  there  are  flanking  truss  spans,  and  tlie  dotted  lines  when  there  are 
no  flanking  truss  spans.  The  crosses  on  the  bascule  plots  indicate  bridges 
for  which  there  were  complete  weight-records,  and  the  circles  refer  to 
structures  for  which  there  were  full,  detailed  estimates. 

These  plots  give  fair,  average  curves  for  the  quantities  in  both  the 
vertical  Uft  and  the  bascule,  all  in  percentages  of  the  weight  of  a  simple 
span  of  the  same  length  and  carrying  capacity,  fhis  basis  of  comparison 
was  adopted  because  it  ehminates  the  effect  on  the  moving  span  of  different 
live  loads,  different  specifications,  and  different  weights  of  decks.  Also, 
the  percentages  derived  in  this  manner  can  be  applied  with  fair  accuracy  to 
highway  bridges.  These  curves  made  it  a  comparatively  simple  matter 
to  contrast  the  costs  of  the  sai)erstructures  of  the  two  types. 

The  curves  of  Fig.  306  arc  drawn  for  vvell-designod  bridges,  and  do  not 
represent  the  lightest  structures  of  these  types  that  it  is  possible  to  build. 
The  factors  of  safety  of  the  wire  ropes  of  the  vertical-lift  bridges  have  been 
taken  somewhat  larger  than  the  author,  from  his  own  experience,  con- 
siders necessary,  in  order  to  meet  somewhat  the  desires  of  railway  bridge 
engineers. 

For  swing  spans  the  data  given  in  Chapter  LV  of  "Bridge  Engineering," 
supplemented  by  other  data  in  the  author's  office,  proved  ample. 

There  were  also  available  the  complete  quantities  for  the  double-leaf 
trunnion-bascule  recently  designed  by  the  author's  firm  for  the  highway 
bridge  over  the  Housatonic  River,  and  those  for  the  single-leaf,  Brown- 
balance-beam-bascule  highway-l)ridge  over  the  iNTystic  Kiver.  A  vertical- 
lift  bridge  was  estimated  for  each  location,  and  the  results  compared. 


ECONOMICS   OF   MOVABLE    SPANS 


299 


When  contrasting  the  vertical  hfts  and  the  heel-trunnion  bascules,  it 
was  assumed  that,  for  low  vertical  clearances,  the  lengths  of  moving  spans 
would  be  the  same  in  the  two  types,  the  fenders  being  placed  as  close  to 
the  piers  as  possible.  Since  the  bascule  can  rarely  be  rotated  through 
more  than  83  or  84  degrees,  a  vertical  Une  through  the  face  of  the  fender 

50        100        150       200       250 


100        150       ZOO        250         0         50         100        150       200 
Leof'fh  o/ bascule  Span  in  fee/  ^  Sear  fo{  Trunnion    Verfica/  Move  me  of  of  [iff  5pan  in  Feef. 

Fig.  306.     Percentage  Weights  for  Double-Track-Railway,  Vertical-Lift  Bridges  and 
Single-Leaf,  Heel-Trunnion  Bascules. 

near  the  trunnion  will  generally  intersect  the  bottom  chord  of  the  fully- 
raised  span  at  dome  height  above  the  water.  This  height  will  depend  upon 
the  horizontal  distance  from  the  trunnion  to  the  said  vertical  Une,  the 
height  of  the  trunnion  above  the  bottom  chord,  and  the  angle  of  inclination 
of  the  said  chord  to  the  vertical;   but  it  will  generally  be  about  50  or  60 


300 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XXX 


feet.  For  clear  heights  much  exceeding  these,  the  bascule  leaf  will  have 
to  be  longer  than  the  vertical-lift  span,  unless  an  encroachment  on  the 
clearance  at  one  corner  be  permitted,  which  is  not  usually  the  case.  For  a 
clear  height  of  150  feet,  this  excess  length  will  generally  be  at  least  10  or 


1 

l' 
(-' 

/ 

A 

-  1 

-K 

^, 

^\ 

/- 

Xm 

\ 

/So  'cfeor        1 

40' 

'■          ns'          1 

7f^'                 J 

Vertical-Lift  Bridge  Heel-Trunnion  Bascule 

Fig.  30c.     Layouts  with  No  Flanking  Truss-Spans. 


1 

• 

m' 

i          /So  'c/eor        1 

1 

/Si' 

1 

1 

/7S' 

\, 

57/' 

-1 

\' 

^ 

Hccl-Trunnion  Bascule 

Fio.  30(i.     Layouts  with  Flanking  Tniss-Simns. 

12  feet,  and  often  still  more.     This  limitation  does  not  apply  to  the  Brown 
balance-beam  type,  which  can  be  rotated  90°. 

In  making  the  comparisons,  it  was  necessaiy  to  consider  two  cases — 
fn-st,  when  there  ai'c  long  flanking-spans,  and,  second,  when  there  are  not. 
Typical  layouts  are  shown  in  Figs.  80c  and  30d.     It  will  be  noted  that  in 


ECONOMICS   OF  MOVABLE   SPANS  301 

each  comparison  the  total  length  of  bridge  considered  is  the  same.  The 
substructure  was  designed  for  several  cases — piers  on  rock  at  various 
depths,  piers  on  deep-sand  foundations,  and  piers  on  piles  loaded  to  the 
limit  of  30  tons  each.  Calculations  were  made  for  clear-channel  widths  of 
100  feet,  150  feet,  200  feet,  and  250  feet. 

For  the  layouts  shown  on  Fig.  30c,  in  which  there  is  the  same  number  of 
piers  in  the  two  cases,  it  was  found  that  ordinarily  the  substructure  costs 
nearly  the  same  for  the  two  types.  In  some  instances  the  vertical-lift 
substructure  was  cheaper,  while  in  others  that  of  the  bascule  was  a  trifle 
more  economic.  The  comparison  for  these  layouts,  consequently,  is  almost 
entirely  a  question  of  superstructure  costs.  For  the  layouts  shown  in  Fig. 
30(i,  the  bascule  substructure  is  always  the  more  expensive,  so  that  both 
substructure  and  superstructure  must  be  considered. 

Fig.  30e  gives  comparative  costs  for  double-track-railway-bridges 
designed  for  Class  60  loading.     The  following  unit  prices  were  used: 

Structural  metal  in  spans 8^  per  lb. 

Structural  metal  in  towers,  counterweight  trusses,  etc...  .    10^     '^ 

Machinery  of  all  kinds 40^     "' 

Counterweights $30  per  cu.  yd. 

Pier  shafts $20    " 

Pier  bases $40  to  $60    " 

The  lower  group  of  curves,  for  layouts  such  as  shown  in  Fig.  30c,  gives 
superstructure  costs  only;  while  the  upper  group,  for  layouts  such  as  indi- 
cated in  Fig.  SOd,  records  the  total  cost  of  superstructure  and  substructure, 
with  the  piers  resting  on  piles.  The  comparison  for  the  latter  substructure 
condition  gives  average  results,  and  was  therefore  adopted.  For  other 
types  of  substructure  the  relative  costs  differ  but  slightly,  excepting  that 
the  bascule  is  considerably  more  costly  with  deep  or  expensive  foundations. 
The  full  hues  for  the  bascule  costs,  noted  "Clear  Height  50  ft.  or  less," 
apply  for  greater  heights  when  an  encroachment  on  the  corner  of  the 
clearance  diagram  is  permitted. 

Fig.  30/  gives,  for  various  clear-channel  widths,  the  vertical  clearances 
at  which  the  vertical-lift  bridge  will  just  equal  the  bascule  in  cost.  This 
is  shown  for  layouts  both  with  and  without  long  flanking-spans.  The 
two  full  lines  apply  for  clear  heights  up  to  50  feet,  and  for  greater  heights 
when  an  encroachment  on  the  corner  of  the  clearance  diagram  is  allow- 
able; while  the  two  dotted  lines  are  for  greater  heights  with  no  encroach- 
ment permitted. 

In  working  up  the  curves  of  Figs.  SOd  and  30e,  it  was  assumed  that  the 
distance  from  center  to  center  of  piers  exceeds  the  clear  channel  by  from 
20  to  30  feet,  and  that  the  clearance  above  the  water  line  is  20  feet  when 
the  moving  span  is  down.  With  a  smaller  down-clearance  than  this, 
the  clear  heights  at  which  the  types  are  equal  will  be  reduced;  and  with  a 
greater  down-clearance  it  will  be  increased. 


302 


ECONOMICS  OF  bridgework: 


Ch.\pter  XXX 


The  curves  of  Figs.  30e  and  30/  are  based  upon  the  assumption  that, 
for  the  vertical  hft  span,  the  motors,  operating  machinery,  and  machinery 
house  are  located  on  the  moving  span,  thus  increasing  the  weight  of  the 
said  span  by  10  per  cent  or  more.  While  this  is  the  ideal  location  for  this 
machinery,  especially  when  the  operator  is  on  the  span,  it  is  considerably 


140 


160       130       200       Z20 
C/ear  Channe/  in  Feef 


240       260       2(30      JOO 


Fig.  30e. 


Comparative  Costs  of  Double-Track-Railway,   Vertical-Lift  Bridges  and 
Single-Leaf,  Heel-Trvmnion  Bascules. 


cheaper  to  place  the  said  machinery  in  the  towers.  If  this  be  done,  the 
clear  heights  at  which  the  cost  of  the  vertical  lift  will  just  equal  that  of 
the  bascule  will  be  increased  10  feet  or  more;  but  the  author  has  plotted 
th(!  cui-ves  on  the  other  basis,  because  he  considers  the  additional  cost 
justified. 


ECONOMICS   OF   MOVABLE    SPANS 


303 


The  curves  do  not  apply  to  skew  layouts.  If  in  these  the  piers  are  to 
be  square,  Fig.  30/  can  be  used  by  making  a  layout  and  finding  the  required 
distance  from  center  to  center  of  piers,  subtracting  therefrom  a  length 
varying  from  20  feet  for  a  100-foot  span  to  30  feet  for  a  200-foot  span,  and 
entering  the  diagram  with  the  result  as  the  "clear-channel"  width.     If 


60 


100       IZO       140       160       180       ZOO       220      240      260, 
C/ecrr    C/xjnne/    in   feef 


Fig.  30/.     Clear  Channels  and  Clear  Heights  for  Equal  Costs  of  Double-Track-Railway, 
Vertical-Lift  Bridges  and  Single-Leaf,  Heel-Trunnion  Bascules. 


skewing  piers  is  permissible,  both  can  be  skewed  for  the  vertical  lift,  but 
only  the  rest-pier  for  the  bascule.  This  condition  favors  the  vertical  lift 
materially. 

For  deep  and  expensive  piers,  a  bascule  layout,  such  as  is  shown  in 
Fig.  30d!  is  not  economic,  that  indicated  in  Fig.  Z^g  being  cheaper.     The 


304 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XXX 


two  layouts  shown  in  the  latter  figure  were  next  compared.  It  was 
found  that,  whereas,  for  the  layouts  of  Fig.  30d,  the  bascule  and  the  ver- 
tical lift  were  of  equal  cost  for  a  clear  height  of  about  170  feet,  for  the 
layouts  of  Fig.  30g  they  would  be  equal  for  a  clear  height  of  125  feet  with 


Vertical-Lift  Bridge 


Heel-Trunnion  Bascule 
Fig.  30^.     Layouts  with  Flanking  Truss-Spans — ^Bascule  Tower  Cantilevered. 

rock  foundations,  and  for  one  of  180  feet  with  deep-sand  or  pile  founda- 
tions. 

In  order  to  illustrate  the  use  of  the  curves  of  Figs.  306,  30e,  and  30/, 
the  following  jjroblems  and  their  solutions  are  given: 


Example  No.  1 

What  are  the  quantities  of  superstructure  materials  in  a  bascule  and 
in  the  corresponding  vertical-lift  span  for  a  Class  60,  double-track-railway 
l)ridgc,  the  span-lengths  being  those  in  Fig.  30c,  the  clearances  above  high 
water  being  20  feet  with  span  down  and  150  feet  with  span  raised  to  full 
height,  and  the  bascule  span  being  permitted  to  encroach  in  one  corner  of 
the  waterway  clearance? 


ECONOMICS   OF  MOVABLE   SPANS  305 

Distance  center  to  center  piers =   175  feet 

Distance   center  to   center  of 

bearings  of  movable  span, ...  '  =   170  feet 

Vertical  movement  of  lift  span .  (=150-20  [=   130  feet 

Weight  of  170-ft.  fixed  span. 

Deck     900^X175  =   158,000  lbs. 

Metal 4,630X170  =  787,000  lbs. 

Total 945,000  lbs. 

Vertical-Lift  Bridge: 
Structural  metal. 

Lift  span 787,000+945,000X0. 13  =      910,000  lbs. 

Tower  floor-systems 2X1,320X40  =       105,000  lbs. 

Total  span  metal ....         1,015,000  lbs. 

Towers  and  counterweight 

steel 945,000X0.80  =      760,000  lbs. 

Total 1,775,000  lbs. 

n       ,         •  K+                       945,000X1.20  _^  , 

(counterweights ^j— =      300  cu.  yds. 

Machinery  and  ropes 945,000  X  0 .  20  [=      190,000  lbs. 

Bascule: 

Structural  metal: 

Bascule  span 787,000+945,000X0.04  =      825,000  lbs. 

Tower     floor-system    and 

approach  span 2X1320X40  =       105,000  lbs. 

Total  span  metal =      930,000  lbs. 

Towers,      counterweight 

trusses,    etc 945,000X1.04  =      980,000  lbs. 

Total =   1,910,000  lbs. 

n       +         .  ,  ,                       945,000X2.60  „.„  , 

Counterweights =       640  cu.  yds. 

Machinery  and  trunnions.   945,000X0.15  =       142,000  lbs. 

It  will  be  noted  from  the  foregoing  that  the  estimator  must  be  able  to 
figure  independently  the  weights  of  the  170-foot  fixed  span,  the  tower  floor- 
systems,  and  the  approach  spans.  The  curves  of  Chapter  LV  of  "Bridge 
Engineering"  can  be  used  for  this  purpose. 


806  ECONOMICS   OF   BRIDGEWORK  Chapter  XXX 

Example  No.  2 

In  the  preceding  example,  what  would  be  the  comparative  costs  of  the 
two  superstructures,  using  the  unit  prices  for  materials  in  place  which 
were  employed  in  working  up  Fig.  30e. 

Vertical  Lift: 

Deck 510  lin.  ft.    @  $10  $5,100 

Metal  in  spans 1,015,000  lbs.        @     8j^  81,200 

Metal  in  towers,  etc 760,000  lbs.        @  \0i  76,000 

Counterweights 300  cu.  yds.  @  $30  9,000 

Machinery  and  ropes 190,000  lbs.         @  40ji  76,000 

Elec.  equip,  and  houses 20,000 

Total $267,300 

Bascule: 

Deck. : 510  lin.  ft.    @  $10  5,100 

Metal  in  spans 930,000  lbs.         @       8^  74,400 

Metal  in  towers,  etc 980,000  lbs.         @     10^  98,000 

Counterweights 640  cu.  yds.  @  $30  19,200 

Machinery  and  trunnions 142,000  lbs.         @     40^  56,800 

Elec.  equip,  and  houses 20,000 

Total $273,500 

Entering  the  lower  group  of  curves  of  Fig.  30e  with  a  150-foot-clear 
height  for  the  vertical  lift,  we  find  the  cost  to  be  $270^000 ;  while  entering 
it  with  a  150-foot  channel  and  a  clear  height  of  "50  feet  or  less"  for  the 
bascule  (because  encroachment  on  one  corner  of  the  waterway  clearance 
is  permitted),  we  read  $272,000  as  the  cost  of  the  bascule.  The  margin 
in  favor  of  the  vertical  lift  is,  therefore,  given  as  $2,000  by  Fig.  30e,  and  as 
$6,200  by  the  figures  derived  from  the  more  accurate  curves  of  Fig.  306, 
which  is  a  satisfactory  check, 

Exam-pie  No.  3 

What  are  the  comparative  costs  of  a  double-track-railway.  Class  60, 
bascule  and  the  corresponding  vertical  lift  for  a  180-foot  clearropening 
flanked  by  fixed  truss  spans,  the  clear  height  required  being  135  feet  when 
the  span  is  raised  and  15  feet  when  the  span  is  down,  the  bascule  being 
permitted  to  encroach  on  one  corncn-  of  the  waterway  clearance. 

For  the  vertical-lift  span,  we  must  enter  the  upper  group  of  curves  in 
Fig.  30^  with  a  "clear  height"  of  135-15+20=  140  feet;  for  that  diagram 
is  plotted  for  a  clear  height  of  20  feet  with  span  down.     For  a  180-foot 


ECONOMICS   OF  MOVABLE   SPANS 


307 


channel,  we  find  the  cost  to  be  $770,000.     For  the  bascule,  we  enter  with  a 
"clear  height"  of  "50  feet  or  less,"  and  find  the  cost  to  be  $820,000. 

Example  No  4 

What  would  be  the  comparative  costs  in  Example  No.  3,  if  the  bascule 
were  not  permitted  to  encroach  on  one  corner  of  the  waterway  clearance? 

The  cost  for  the  vertical  lift  is  $770,000  as  before.  Entering  Fig.  30e  for 
the  bascule  with  a  "clear  height"  of  140  feet,  by  interpolating  we  find  the 
cost  to  be  about  $845,000. 

Example  No.  5 

What  are  the  comparative  costs  of  a  double-track-railway,  Class  60, 
bascule  and  the  corresponding  vertical  lift  for  a  120-foot  clear-opening 
without  flanking-spans,  the  "clear  height"  being  50  feet  with  span  raised, 
and  20  feet  with  span  down? 

From  the  lower  group  of  curves  in  Fig.  30e,  we  find  the  cost  of  the 
vertical  Hft  to  be  $170,000,  and  that  of  the  bascule  $200,000. 


Example  No.  6 

What  would  be  the  comparing  costs  for  Example  No.  5,  if  flanking  truss 
spans  were  used? 

Entering  the  upper  group  of  curves  of  Fig.  30e,  we  find  $460,000  for 
the  vertical  lift,  and  $497,000  for  the  bascule. 

Example  No.  7 

In  a  double-track-railway  bridge,  with  flanking  truss  spans,  having  a 
clearance  above  high  water,  with  span  down,  of  20  feet,  what  will  be  the 
vertical  clearances  for  a  vertical-lift  span  of  equal  cost  with  a  bascule,  when 
the  clear  horizontal  opening  is  100  ft.,  110  ft.,  120  ft.,  or  130  ft.? 

From  Fig.  30/  we  find  the  following: 


Horizontal 
Clearance 

Vertical  Clearance 

Bascule  Permitted 

to  Encroach  on 
Corner  of  Clearance 

Bascule  not  Permitted 

to  Encroach  on 
Corner  of  Clearance 

100' 
110' 
120' 
130' 

100' 
115' 
129' 
145' 

116' 
143' 
170' 
197' 

308 


ECONOMICS   OF  BRIDGEWORK 


Chapter  XXX 


Example  No.  8 

What  would  be  the  results  in  Example  No.  7  in  case  there  were  no  flank- 
ing truss  spans? 

From  Fig.  30/  we  have  the  following: 


Horizontal 
Clearance 

Vertical  Clearance 

Bascule  Permitted 

to  Encroach  on 
Corner  of  Clearance 

Bascule  not  Permitted 

to  Encroach  on 
Corner  of  Clearance 

100' 
110' 
120' 
130' 

SO' 

93' 

106' 

120' 

90' 
115' 
140' 
165' 

Comparisons  were  made  for  swing  bridges  giving  two  150-foot  channels 
and  two  200-foot  channels,  as  against  one  channel  of  150  and  one  of  200 
feet  for  the  vertical  lift  and  the  bascule.  It  was  found  that  the  swing  was  a 
trifle  more  expensive  than  the  bascule  for  the  150-foot  channel,  and  of 
about  the  same  cost  for  the  200-foot  channel.  For  clear  heights  less  than 
160  feet,  the  vertical  hft  was  cheaper  than  the  swing.  There  was  some 
variation  with  the  depth  of  the  fouijdations,  the  swing  being  more  expensive 
for  deep  ones. 

The  Mystic  River,  Brown-Balance-Beam  bascule  is  a  through,  plate- 
girder,  highway  bridge  215'  3"  long,  consisting  of  a  fixed  span  of  68'  6",  a 
tower  span  of  23'  9",  a  bascule  span  of  88'  0",  and  a  fixed  span  of  35'  0". 
The  clear  channel  is  75'  0".  This  layout  was  compared  with  one  for  a 
vertical  lift,  consisting  of  one  92'  3"  fixed  span,  one  88'  0"  hft  span,  and  one 
35'  0"  fixed  span.  It  was  found  that  the  two  were  of  equal  cost  when  the 
required  vertical  movement  of  the  lift  span  was  61',  corresponding  to  a 
clear  height  of  64',  since  there  is  only  a  three-foot  clearance  when  the  span 
is  down.  If  the  clearance  with  span  down  had  been  the  usual  one  of  15  or 
20  feet,  the  two  types  would  have  been  equal  for  a  clear  height  of  75  or  80 
feet.  This  Brown  bascule  rotates  through  90°,  so  that  the  moving  span 
never  needs  to  be  any  longer  than  that  of  the  vertical  lift. 

The  Housatonic  River  Bridge  is  a  concrete-arch  structure,  with  a  simple- 
trunnion,  double-leaf -bascule  span  giving  a  clear  waterway  of  125',  the 
distance  from  center  to  center  of  trunnions  being  175'.  The  bascule  piers 
wore  necessarily  quite  heavy  and  mnssive;  and  while  much  lighter  ones 
would  have  sufficed  for  the  vertical  lift,  it  was  decided  to  make  a  compari- 


ECONOMICS   OF   MOVABLE    SPANS  309 

son  with  the  same  sized  shafts,  reducing  the  pile  bases  for  the  smaller  loads 
of  the  vertical  lift.  This  was  the  most  favorable  assumption  for  the  bas- 
cule. It  was  found  that  the  two  types  were  of  equal  cost  for  a  clear  height 
of  180  feet,  corresponding  in  this  case  to  a  vertical  movement  of  155  feet 
for  the  lift  span. 

It  has  long  been  the  author's  surmise  that  where  the  clear  height 
required  does  not  exceed  the  clear  width  of  channel,  the  vertical  Uft  would 
always  be  cheaper  than  the  bascule.  The  curves  of  Fig.  30/  show  this  to  be 
true  when  the  bascule  is  not  permitted  to  encroach  on  one  corner  of  the 
clearance.  For  cases  where  such  encroachment  is  permissible,  the  state- 
ment is  always  true  for  bridges  with  flanking-spans,  and  practically  so  for 
bridges  without  flanking-spans. 

It  would  be  very  valuable  to  extend  this  investigation  to  cover  short 
spans,  where  the  bascule  would  usually  be  of  the  trunnion  type  with  either 
the  underneath  or  the  overhead  counterweight,  or  of  the  rolhng-lift  type; 
while  the  vertical  hft  would  have  two-leg  towers  with  over-head-bracing 
trusses.  However,  an  investigation  of  this  sort  would  require  more  data 
than  those  at  the  author's  disposal.  From  comparisons  made  in  the  past, 
it  is  evident  that,  for  such  short  spans,  with  the  standard  low  clearances 
of  the  inland  waters  the  vertical  Uft  will  almost  always  be  the  cheaper,  while 
with  the  high  clearances  required  along  the  coast  one  of  the  bascule  types 
will  be  more  economic. 


CHAPTER  XXXI 

ECONOMICS    OF   OPERATING   MACHINERY   AND    POWER 

The  data  for  this  chapter  were  furnished  mainly  by  the  author's  old 
friend  and  occasional  associate  in  professional  work,  Thomas  Ellis  Brown, 
Mem.  Am.  Soc.  C.  E.;  but  some  valuable  suggestions  as  to  items  to  be 
considered  were  given  by  Major  Leon  L.  Clarke, who,  for  many  years  before 
the  Great  War  and  for  a  short  time  after  his  return  from  France,  where  he 
rendered  effective  and  distinguished  service  to  the  Allied  Cause,  was  the 
author's  principal  assistant  mechanical  engineer,  and  as  such  devoted  his 
entire  attention  to  the  designing  and  installation  of  machinery  for  operat- 
ing movable  spans. 

As  long  ago  as  1892,  when  the  author  was  retained  by  the  City  of 
Duluth,  Minn.,  on  his  first  design  for  a  vertical-lift  bridge,  he  recognized 
the  necessity  for  some  expert  aid  in  solving  certain  important  mechanical 
problems;  and,  consequently,  he  looked  the  country  over,  in  order  to  find 
the  highest  American  authority  on  the  mechanics  of  lifting  great  weights. 
The  result  of  his  search  proved  that,  even  at  suCh  an  early  date,  Mr.  Brown 
was  universally  acknowledged  to  be  the  best  authority  on  elevators  and 
their  machinery;  and,  therefore,  the  author  retained  him.  From  that 
incident  there  resulted  a  friendship  and  a  somewhat  desultory  association 
which  have  proved  very  satisfactory  and  beneficial  to  both  parties  thereto. 

With  the  help  of  two  such  experts  as  Mr.  Brown  and  Major  Clarke 
the  author  feels  that  he  has  done  his  best  to  treat  one  of  the  most  difficult 
branches  of  engineering  economics. 

The  kind  of  power  and  type  of  machinery  suitable  for  the  operation  of 
movable  bridges  depend  greatly  upon  the  nature  of  the  design  of  the  struc- 
ture, the  available  space  for  apparatus,  and  the  local  conditions  of  fuel  or 
power  supply,  and  are,  therefore,  contingent  upon  the  ruling  features  of 
the  particular  case;  hence  no  hard-and-fast  rules  of  economics  therefor 
can  be  formulated.  On  that  account  the  contents  of  this  chapter  will  be 
limited  to  a  dissertation  concerning  general  conditions  and  the  offering  of  a 
few  pertinent  suggestions. 

The  selection  of  motive  power  is  largely  dependent  on  the  location  of  the 
bridge  with  relation  to  sources  of  power-sup])ly.  When  located  in  or  near 
a  large  city  or  town,  electric  current,  either  direct  or  alternating,  is  ahnost 

310 


ECONOMICS   OF   OPERATING   MACHINERY   AND   POWER  311 

always  available;  and,  when  purchasable  at  reasonable  meter-rate,  it  is 
usually  the  most  convenient  and  economic  type  of  energy  to  adopt.  For- 
merly, electricity  not  being  available,  steam  was  invariably  used,  and  boilers 
were  installed  on  or  near  the  bridge.  This  involved  the  handling  of  coal, 
disposition  of  ashes,  and  continuous  maintenance  of  steam  pressure;  and 
it  was  usually  found  that  the  fuel  expense  was  nearly  constant  and  almost 
entirely  independent  of  the  number  of  movements  of  the  bridge.  The 
author  knows  of  bridges  where  steam  is  maintained  during  long  periods  of 
inactivity,  and  during  periods  of  practically  closed  navigation,  thus  render- 
ing the  operation  excessively  uneconomic.  It  is  evident  that  a  form  of 
power  which  may  be  paid  for  only  as  usefully  expended  is  of  true  economic 
value.  In  some  large  cities  of  Europe  hydraulic  pressure  or  compressed 
air  is  purchasable  by  meter;  and  bridges  erected  within  reach  of  such 
pressure  systems  can  most  advantageously.be  operated  thereby,  as  these 
types  of  power  give  a  smooth  and  perfect  control  attainable  in  no  other  way. 
In  the  United  States,  however,  we  are  confined  practically  to  two  sources 
of  power  other  than  steam,  viz.,  electric  current  and  the  internal  combus- 
tion engine;  and  as  electricity  is  quite  generally  available,  it  is  most 
commonly  used,  but  few  instances  existing  where  internal  combustion 
engines  are  employed  alone  as  the  primary  motive  power,  though  quite 
often  as  auxiliaries  for  emergency  use. 

With  the  great  improvement  reached  in  the  design  and  construction 
of  the  high-speed,  multi-cylinder  engine  of  the  present  day,  there  seems  to 
be  no  good  reason  for  its  limited  employment  in  the  operation  of  bridges. 
In  many  cases  the  cost  of  transmission  lines,  transformers,  and  other  par- 
aphernalia necessary  to  convey  electric  current  to  the  bridge  site,  would 
exceed  the  cost  of  such  engines,  while  the  fuel  for  them  is  obtainable  at 
almost  any  cross-roads,  consequently  true  economics  demands  their  more 
extensive  use. 

Efficiency,  as  commonly  understood,  i.e.,  ratio  of  power  output  to 
power  input,  rarely  needs  consideration  in  the  economics  of  movable 
bridges,  as  the  time  of  motion  is  generally  not  much  over  a  minute,  or  at 
most  two  minutes,  in  one  direction,— say  on  an  average  three  minutes  per 
cycle;  and  comparatively  few  bridges  are  called  upon  to  open  more  than 
10  or  20  times  per  day  on  an  average  throughout  the  year.  Thus  the  total 
yearly  working  time  of  a  fairly-active  bridge  will  ordinarily  amount  to  less 
than  75  actual  days  of  motion,  the  power  consumed  being  mainly  that 
required  for  starting  and  stopping;  and,  therefore,  efficiency  as  above 
defined  is  of  but  little  importance.  True  economics  demands  the  selection 
of  power  and  machinery  from  the  standpoint  of  as  great  simplicity  and 
low  first  cost  as  is  consistent  with  robustness  and  durabihty,  and  especially 
with  positiveness  and  ease  of  control. 

In  the  earlier  days  of  electric  supply  (and  this  condition  may  possibly 
apply  in  a  few  localities  today)  it  was  customary  to  charge  a  flat  monthly 
or  yearly  rate  for  current,  based  on  the  peak  load  of  the  motors  used,  with- 


312  ECONOMICS   OF  BRIDGEWORK  Chapter  XXXI 

out  regard  to  the  actual  amount  of  current  consumed ;  and,  should  such  a 
case  arise,  other  forms  of  power  should  be  carefully  considered. 

When  electricity  is  purchasable,  the  consumer  is  usually  confined 
to  the  kind  of  current  the  producing  company  will  supply,  and,  therefore, 
has  no  choice  between  alternating  and  direct  current;  but  whenever  such 
a  choice  exists,  direct  current  should  have  the  preference,  as  giving  much 
greater  latitude  in  motor  speeds,  and,  consequently,  tending  to  economy 
in  cost  of  gearing,  and,  more  important  still,  as  giving  a  much  more 
flexible  and  perfect  control,  especially  when  shunt-wound  fields  are 
used,  providing  automatic  speed-control  under  positive  and  negative 
loadings. 

The  more  usual  sizes  of  movable  bridges,  reqmring  motors  of  from  30  to 
100  H.P.,  when  located  adjacent  to  electric  plants  of  reasonable  size,  may, 
preferably,  be  operated  directly  from  the  fine,  if  the  current  be  of  low  ten- 
sion, or  through  transformers  when  it  is  of  high  tension;  but  cases  may 
arise,  especially  with  bridges  of  very  large  size,  where  the  power  station  or 
the  transmission  fines  cannot  stand  the  starting  current  or  peak  load 
required.  In  such  cases  some  form  of  accumulator  must  be  used  to  extend 
the  current  draught  over  a  longer  time,  so  that  the  motors  may  be  relatively 
small  and  within  the  capacity  of  the  power  supply.  Electric  accumulators 
(storage  batteries)  may  be  used,  and  the  apparatus  may  be  entirely  elec- 
trical; but  such  cases,  in  the  author's  opinion,  offer  an  excellent  opportunity 
for  the  use  of  hydraufic  power  for  the  direct  mos^ement  of  the  bridge,  the 
primary  electric  power  being  employed  to  produce  and  store  hydraulic 
pressure  in  suitable  accumulators.  This  system  may  be  employed  also  in 
cases  where  gasofine  engines  are  desired  and  where  engines  of  sufficient 
eize  to  operate  the  bridge  directly  would  be  inconvenient  or  impracticable; 
as  comparatively  small  engines  could  be  used  to  store  hydraulic  power  or 
compressed  air  in  suitable  accumulators. 

The  conveyance  of  power  from  the  driving  motor  or  engine  to  the 
bridge  itself  is  usually  accomplished  by  gearing,  the  direct  connection  to 
the  bridge  being  by  means  of  gear  teeth  in  the  form  of  strutted  racks  pivoted 
to  the  bridge,  or  by  means  of  curved  segments,  forming  a  gear  wheel  of 
large  radius  bolted  directly  to  the  bridge  girders;  and,  in  the  case  of  ver- 
tical-lift bridges,  by  means  of  ropes  connected  to  the  towers  and  woimd 
upon  drums  carried  on  the  moving  span. 

In  all  of  these  cases,  as  the  movement  of  the  span  is  slow  in  comparison 
with  the  speed  of  the  motor  or  engine,  long  trains  of  spur  gearing  are  neces- 
sary; and  the  motor  or  engine  should  be  of  as  slow  speed  as  practicable  in 
order  to  reduce  the  amount  of  gearing  to  a  minimum. 

Thus  a  bascule  bridge,  operating  through  ixhout  90°  in  one  and  a  half 
minutes,  moves  at  a  speed  approximately  equivalent  to  l  of  a  revolution  per 
minute;  and  to  gear  this  to  a  motor  running  at,  say,  600  R.P.M.  means  a 
total  specnl  icMhiction  of  3()()0:1.  For  that  i-eason,  the  primary  reduction 
directly  at  the  moving  span  should  be  as  great  as  practicable,  i.e.,  the  main 


ECONOMICS   OF   OPERATING   MACHINERY   AND    POWER  313 

pinion  should  have  the  minimum  number  of  teeth  consistent  with  strength 
and  smooth  running,  and  the  rack  should  have  as  large  a  radius  as  the 
design  and  dimensions  of  the  bridge  will  permit.  In  the  case  of  vertical- 
lift  bridges  operated  by  ropes  wound  on  drums,  a  considerable  saving  in 
amount  of  spur  gearing  can  be  made  by  running  the  operating  ropes  over 
pulleys,  forming  a  tackle,  whereby  a  ratio  of  2,  3,  4,  or  even  more  could  be 
obtained  by  the  roping  alone. 

Much  spur  gearing  in  many  cases  could  be  eliminated  by  the  use  of 
worm  gearing,  which,  with  the  perfection  of  workmanship  now  attained,  is 
far  more  efficient  than  commonly  supposed;  and,  in  general,  it  may  be 
stated  that  the  efficiency  of  a  well-designed  and  properly-cut  worm-gear 
will  be  higher  than  that  of  its  equivalent  in  spur  gearing.  It  is  believed 
that  worm  gearing  could  be  introduced  advantageously  in  many  cases,  in 
order  to  reduce  the  amount  of  gearing,  or,  on  the  other  hand,  to  increase 
the  speed-ratio  and  enable  smaller  and  higher-speed  motors  to  be  employed. 
Incidentally,  the  introduction  of  worm  gearing  would  eliminate  the  noise 
of  the  high-speed,  steel  spur-gearing  quite  commonly  employed. 

The  modern  multi-cylinder  gasoline  engine  seems  ideal  for  the  operation 
of  movable  bridges,  as  it  probably  combines  the  greatest  power  and  econ- 
omy of  operation  with  the  least  first  cost,  weight,  and  space;  but  it  has  not 
been  used  extensively  on  bridges  on  account  of  its  high  speed,  800  to  1200 
R.P.M.  or  more,  and  the  consequent  large  speed-reduction  necessitated — 
also  on  account  of  the  requirement  for  friction  clutches  to  enable  the  engine 
to  be  thrown  into  and  out  of  gear,  because  such  engines  must  be  started 
before  beginning  to  move  the  bridge,  and  must  be  run  continuously  during 
the  cycle  of  operations.  These  difficulties  can  be  overcome  by  the  use  of  a 
hydraulic  reducing-gear  attached  to  the  engine  shaft  and  in  turn  driving  a 
worm  gear.  By  such  an  arrangement  the  clutches  are  eliminated,  and  a 
speed  reduction  of  from  40  :  1  to  100  :  1  may  be  obtained  at  once  and  the 
remaining  reduction  be  made  with  a  short  train  of  gears. 

The  author  believes  the  ideal  apparatus  would  be  two  high-speed  gaso- 
line engines,  each  with  hydraulic  transmission  gear  and  worm  gear,  the  two 
engines  together  of  sufficient  power  to  operate  the  bridge  at  the  maximum 
required  speed,  and  one  alone  (by  means  of  the  hydraulic  reducing  gear) 
capable  of  running  it  at  slower  speed.  A  third  engine,  smaller  than  the 
others,  should  be  used  to  compress  air  for  air  brakes,  to  work  end  locks  and 
rail  locks,  and  to  circulate  cooling  water  for  the  transmission  gears.  The 
third  or  smaller  engine  could  be  arranged  to  be  thrown  into  gear  and  used  as 
an  emergency  engine,  in  the  event  of  complete  break-down  of  the  main 
engines,  so  as  to  operate  the  bridge  at  very  slow  speed;  and  it  could  also  be 
utilized  for  driving  a  small  dynamo  for  signal  and  other  lighting.  Thus  all 
the  functions  of  the  bridge  could  be  performed  by  means  of  gas  engines,  and 
be  made  entirely  independent  of  outside  sources  of  power  supply.  The 
installation  and  care  of  transmission  lines  and  transformers  would  be 
entirely  avoided;   and,  obviously,  the  arrangement  proposed  would  be  of 


314  ECONOMICS   OF   BRIDGEWORK  Ch.^pter  XXXI 

the  greatest  value  in  situations  where  electric  power  is  not  available,  or  not 
obtainable  on  reasonable  terms. 

Movable  bridges  may  be  considered  as  consisting  of  three  main  elements, 
the  first  comprising  the  actual  bridge  or  carrying  structure,  fixed  in  posi- 
tion during  normal  traffic,  and  which  must  be  removed  to  permit  of  trans- 
verse traffic ;  the  second  comprising  means  to  support  the  carrying  structure 
together  with  the  counterweights  required  to  balance  it;  and  the  third 
comprising  means  to  operate  or  impart  motion  to  the  carrying  structure, 
its  counterweights,  and  such  parts  of  the  supporting  structure  as  must 
move  therewith — the  whole  constituting  a  complete  machine. 

Of  this  machine  it  is  convenient  to  classify  those  parts  which  require  to 
be  made  in  the  machine  shop  as  "machinery,"  in  contradistinction  to  those 
fabricatedin  the  bridge  shop  and  classified  as  "structural";  and,  as  machine- 
shop  work  is  much  more  costly  than  structural  work,  economics  requires 
that  the  design  should  aim  at  a  preponderance  of  parts  which  may  be 
finished  in  the  fabricating  shop  and  at  as  complete  a  separation  in  manu- 
facture between  the  machinery  and  structural  parts  as  possible,  and  also 
that  it  should  permit  of  simple  and  easily-adjustable  connections  in  the 
field.  The  vertical-lift  bridge  meets  this  requirement  much  better  than 
does  either  the  swing  or  the  bascule. 

The  carrying  structure  will  consist  essentially  of  structural  steelwork 
and  its  adjuncts,  such  as  flooring,  tracks,  and  the  like,  and  will  comprise 
no  machinery;  the  supporting  structure  will  generally  consist  essentially 
of  structural  steelwork  carrying  such  supporting-machinery  parts  as  trun- 
nions, rollers,  hangers,  sheaves,  and  the  hke;  while  the  operating  machinery 
will  consist  of  actuating-or-retarding-machinerj^  parts,  such  as  gears, 
screws,  rams,  brakes,  buffers,  and  similar  component  elements. 

The  supporting  machinery  parts  are  dependent  for  size  and  strength 
purely  on  the  weights  carried  by  them,  hence  their  cost  is  a  function  of 
the  weight  of  the  movable  masses;  and,  as  they  necessarily  have  slow  and 
limited  motions,  and  as  they  work  under  very  heavy  loads,  they  are 
essentially  costly  and  must  be  designed  for  the  highest  permissible  unit- 
bearing-pressures,  in  order  to  obtain  the  smallest  practicable  diameters. 
In  general,  in  movable  bridges  the  lengths  of  bearings  are  limited  by  space 
conditions,  and  increased  bearing  surface  can  only  be  obtained  by  enlarged 
diameters;  and,  as  the  weights  of  bearings,  trunnions,  etc.,  increase  as 
the  square  of  their  diameters,  and  their  costs  nearly  in  the  same  proportion, 
the  economic  importance  of  high  unit-bearing-pressures  will  be  readily 
understood,  consequently  for  these  parts  one  is  justified  in  adopting  the 
best  grades  of  bearing  metals  and  the  most  complete  provision  for  lubrica- 
tion. The  latter  involves  not  only  suitable  oil-or-grease-grooves,  pressure 
lubricators,  and  lubricant,  all  ai-ranged  so  the  said  lubricant  will  surely 
reach  the  surfaces  under  pressure,  but  also  requires  convenient  and  safe 
means  of  access,  such  as  steps,  ladders,  platforms,  and  raihngs,  as  well  as 


ECONOMICS   OF   OPERATING   MACHINERY   AND    POWER  315 

ample  light  and  space  to  insure  the  comfort  and  safety  of  the  attendants, 
as  parts  dangerous  or  even  difficult  of  access  will  otherwise  almost  surely 
be  neglected. 

The  operating  machinery,  the  function  of  which  is  not  only  to  transfer 
the  motion  of  the  motors  or  prime  movers  to  the  bridge  structure,  but  also 
to  retard  and  arrest  that  of  the  span,  is  dependent  for  the  size  and  strength 
of  its  parts  on  the  power  or  torque  of  the  said  prime  movers  and  the  resist- 
ance of  the  retarding  mechanism  or  brakes;  for  the  maximum  operating 
stresses  to  which  these  parts  will  be  subjected  are  obviously  those  which 
the  motive  power  or  brakes  can  put  upon  them — and  usually  those  pro- 
duced by  the  brakes  are  the  more  severe. 

Breakdowns  of  machinery  rarely  occur  from  the  accelerating  force  of 
the  motive  machine,  while  many  do  occur  from  excessive  retardation  or 
brake  resistance;  and  this  is  easily  accounted  for,  as  the  maximum  torque 
of  the  motive  machine  can  readily  be  determined  and  cannot  be  exceeded, 
while  the  retarding  or  brake  forces  are  dependent  on  frictional  resistances, 
more  or  less  indeterminate,  and  are  liable  to  great  variation  with  slight 
changes  of  condition,  rapidity  of  application,  and  maladjustment,  and 
also  to  a  very  natural  tendency  on  the  part  of  designers  and  operators  to 
provide  unnecessary  brake  strength.  In  the  author's  opinion,  the  oper- 
ating brake-resistance  should  not  exceed  the  starting  torque  of  the  motors. 

Economics,  therefore,  requires  that  the  conditions  of  traffic  should  be 
carefully  studied,  in  order  to  determine  as  nearly  as  possible  the  actual 
service  the  bridge  must  render,  as  well  as  the  resistances  to  motion  likely 
to  be  encountered,  with  the  view  of  avoiding  unnecessarily-great  motive- 
power  with  correspondingly-larger  brake-resistance,  and  consequent 
unnecessarily-high  first-cost  of  machinery  and  motors. 

The  power  and  strength  of  the  operating  machinery,  in  the  case  of 
swing  bridges  having  equal  arms,  is  mainly  a  question  of  speed  of  operation; 
as  it  will  generally  be  found  that  when  the  power  is  sufficient  to  overcome 
the  frictional  resistances  and  give  the  acceleration  needed  to  perform  the 
required  movement  in  the  required  time,  there  will  be  an  ample  amount 
to  overcome  any  unbalance  of  wind  pressure  likely  to  occur  on  the  arms  of 
the  bridge.  Similarly  with  lift  bridges,  if  there  is  ample  power  to  over- 
come the  normal  friction  and  give  the  required  acceleration,  there  will 
be  ample  power  to  overcome  at  full  speed  any  added  friction  on  the  guides 
from  side  wind-pressure,  and,  at  a  slower  speed,  any  unbalanced  load  on 
the  floor,  except,  perhaps,  in  situations  liable  to  unusual  snow  load. 

With  the  bascule  bridge  the  case  is  usually  different  from  that  of  the 
swing  or  the  lift  bridge;  because,  with  the  former  in  a  raised  position,  the 
floor  area  exposed  to  horizontal  wind  pressure  is  large,  especially  in  the 
case  of  the  closed  floors  of  highway  bridges.  The  wind  moment  about 
the  axis  of  a  bascule  bridge  is,  therefore,  great,  while  the  lever  arm  of  the 
operating  machinery  is  usually  comparatively  short;  and  hence  the  pres- 
sures and  forces  in  the  operating  machinery,  as  well  as  the  motive  power 


316  ECONOMICS   OF  BRIDGEWORK  Chapter  XXXI 

required  (and,  consequently,  the  cost),  will  generally  be  determined  by 
the  wind  pressure  to  be  resisted  rather  than  by  time  of  operation  and  accel- 
eration. It  is  thought  that  the  tendency  of  engineers  is  arbitrarily  to 
assume  unnecessarily-high  wind-pressures,  without  regard  to  the  actual 
conditions  and  situations,  and  that,  if  more  careful  studies  of  the  sur- 
roundings were  made,  and  if  the  pressures  provided  for  were  more  m 
accordance  with  those  likely  to  occur  in  actual  practice,  considerable 
economy  would  result. 

The  author  believes  that  in  but  very  few  situations  are  bascule  bridges 
hable  to  be  operated  under  anything  like  such  wind  pressures  as  are  often 
specified,  and  that  due  consideration  is  not  given  to  the  fact  that,  even 
though  the  toe  of  the  span  when  high  in  the  air  may  be  under  considerable 
wind  pressure,  this  pressure  does  not  extend  to  the  heel  of  the  span,  and 
that  on  the  whole  surface  the  total  pressure  is  far  less  than  the  velocity 
of  the  wind  would  seem  to  indicate.  This  is  especially  so  when,  as  is  often 
the  case,  the  banks  are  high,  or  covered  by  trees  or  buildings,  and  the 
bridge  is  sheltered  from  all  but  winds  in  the  direction  of  the  channel.  The 
author  believes,  too,  from  both  his  own  experience  and  conferences  with 
other  bridge  specialists,  that,  in  general,  bascule  bridges  capable  of  slow 
operation  against  a  uniform  pressure  of  ten  pounds  per  square  foot,  or  even 
less,  and  at  full  speed  against  two  pounds  per  square  foot  will  answer  all 
requirements. 

It  is  quite  usual  with  bascule  bridges  to  specify  holding  or  brake  power 
sufficient  to  resist  such  abnormal  wind  pressures  as  fifteen  or  twenty 
pounds  per  square  foot  over  the  whole  floor  surface.  To  meet  such  a 
condition  with  normal  unit  stresses  would  require  excessively-strong 
and  prohibitively-costly  machinery;  and  it  is  believed  that  under  such 
specifications  one  is  warranted  in  using  as  low  factors  of  safety  as  will 
ensure  unit  stresses  within  the  elastic  limit,  for  such  pressures  may  never 
occur  with  the  bridge  raised  during  its  entire  lifetime. 

Such  a  holding  power  requires  a  severity  of  brake  action  not  only  unde- 
sirable but  dangerous  in  normal  operation;  and.  therefore,  if  provision  for 
such  holding  power  must  be  made,  it  should  be  by  means  of  auxiliary 
brakes,  to  be  used  only  in  case  an  emergency  should  arise. 

The  economic  importance  of  the  use,  as  far  as  possible,  of  machinery 
and  apparatus  of  standard  manufacture  cannot  be  too  strongly  empha- 
sized, not  only  in  view  of  the  lower  first  cost,  but  also  in  the  matter  of 
maintenance;  because,  where  special  designs  are  ado]itod  roqiiii-ing  special 
patterns,  those  patterns  must  be  stored  pending  future  repairs,  which, 
occurring  after  long  lapses  of  time,  will  involve  delay  in  the  location  of 
the  required  patterns,  if  they  can  be  found  at  all,  and  extra  expense  and 
time  in  the  reproduction  of  the  parts  from  them.  The  designer  of  the 
bridge,  therefore,  should  provide  ample  space  for  machinery  with  a  view 
to  the  kind  to  })o  installed,  as  often  the  use  of  spcH'inl  ap]iaratus  may  be 
necessitated  by  the  lack  of  a  few  feet  or  even  a  few  inches  of  room. 


ECONOMICS   OF  OPERATING   MACHINERY  AND   POWER  317 

The  author  has  noticed  a  tendency  to  extreme  economy  in  structural 
metal  at  a  sacrifice  of  space  required  for  simplicity  of  machinery.  Struc- 
tural metal  is  cheap  compared  to  machinery;  and,  especially  in  bascule 
bridges,  the  latter  involves  a  large  portion  of  the  total  cost,  hence  a  very 
considerable  apparent  extravagance  in  structural  metal  may  often  result 
in  a  reduction  of  total  expenditure,  by  simplification  of  the  machinery  and 
by  provision  of  space  for  standard  apparatus. 


CHAPTER  XXXII 

POSSIBILITIES   AND    ECONOMICS    OF   THE    TRANSBORDEUK 

Most  of  the  contents  of  this  chapter  are  taken  from  a  paper,  having  the 
same  title,  presented  to  the  Institution  of  Civil  Engineers  of  Great  Britain,* 
but  it  is  supplemented  by  some  later  investigations  concerning  a  proposed 
crossing  of  the  Delaware  River  between  Philadelphia,  Pa.,  and  Camden, 
N.  J.,  on  the  preliminary  economic  studies  for  which  the  author  had  pre- 
viously been  retained. 

The  "transbordeur,"  as  it  was  named  in  France  where  it  was  originated 
by  the  noted  engineer,  Monsieur  F.  Arnodin,  or  "transporter  bridge,"  as  it 
is  called  in  England  where  a  number  of  structures  of  that  type  have  been 
built,  or  the  "aerial  ferry,"  as  it  is  termed  in  the  United  States,  where  there 
is  only  a  single  example,  is  a  rather  inferior  substitute  for  a  low-level 
bridge.  The  author  prefers  to  adopt  the  name  "iranshordeur"  not  only 
because  of  the  prior  claim  of  that  appellation  but  also  on  account  of  its 
being  shorter  than  either  of  the  other  cognomens;  and  he  is  going  to  take 
the  hberty  of  anglicizing  it  hereinafter  by  omitting  to  put  it  in  italics.  The 
only  excuse  for  the  existence  of  this  type  of  structure  is  that  its  construction 
is  permissible  at  certain  locations  where  no  low-level  bridge  would  be 
allowed,  and  where  a  high-level  structure  would  be  unsatisfactory  for  the 
crossing  traffic.  Such  conditions  exist  where  the  land  adjacent  to  the 
waterway  is  low,,  and  where  many  high-masted  vessels  have  to  pass,  or 
where  the  channel  forms  the  entrance  to  a  harbor  of  refuge.  Under  the 
latter  condition,  any  low-level  bridge  might  prove  to  be  a  serious  menace  to 
navigation;  for  it  is  conceivable  that  the  movable  span  might  get  out  of 
order  and  become  immovable  for  a  while  during  a  high  wind  when  vessels 
are  passing  through  the  channel  in  order  to  reach  the  safe  harbor  beyond. 

In  comparison  with  the  low-level  bridge,  the  inferior  features  of  the 
transbordeur  are  as  follows: 

First.  Its  carrying  capacity  for  automobiles  during  any  given  length 
of  time  is  much  smaller. 

Second.  The  time  necessary  for  crossing  by  it,  up  to  the  present  at  least, 
is  much  greater. 

Third.     The  costs  of  both  power  and  labor  for  operation  are  higher. 

Fourth.  While  the  actual  first  cost  of  structure  is  about  the  same,  or 
possibly  a  little  less,  in  respect  to  general  service  rendered  it  is  larger. 

*  The  nontonts  of  this  paper  were  used  by  the  Editor  of  Le  G6nie  Civil  as  the  basis  of 
a  lont^  ('(iiloriiil,  iHiMislicd  in  two  successive  issues. 

318 


POSSIBILITIES    AND    ECONOMICS    OF    THE    TRANSEORDEUR      319 

The  ordinary  transbordeur  consists  of  two  towers,  an  overhead  span 
between  them  high  enough  to  clear  the  masts  of  the  tallest  vessels,  a  single 
track  on  the  span,  a  car  running  upon  the  track,  a  traveling  platform  sus- 
pended from  the  car,  a  fixed  platform  at  each  end  of  the  car's  travel  for 
unloading  and  reloading,  and  approaches  to  these  fixed  platforms  from  the 
streets.  Up  to  the  present  time  all  of  the  transbordeurs  yet  built  are 
single-span,  single-track,  single-carriage,  slow-motion  structures,  con- 
sequently their  efficiency  is  low  and  their  use  is  confined  to  comparatively 
narrow  waterways. 

There  are  four  types  of  bridge  suitable  for  carrying  the  cages  of  the  trans- 
bordeur, viz.,  the  simple-truss,  the  contiruous-truss,  the  cantilever,  and  the 
suspension.  The  choice  between  these  will  depend  almost  entirely  upon 
the  governing  conditions  at  the  crossing. 

In  "Bridge  Engineering"  on  p.  674  the  author  in  1916  wrote  as  follows: 

If  the  author  were  ever  called  upon  to  design  a  transporter  bridge,  he  would  effect 
a  great  improvement  by  widening  the  structure  so  as  to  provide  for  a  double  track, 
and  would  carry  on  it  four  or  more  cars.  These  cars  would  always  travel  upon  the 
right-hand  track,  and  would  run  onto  a  single  track  at  each  end  of  span  where  they 
would  discharge  and  take  on  passengers.  Again,  he  would  use  powerful  electric  motors 
so  as  to  travel  at  high  speed.  By  these  means,  the  carrying  capacity  of  the  bridge  would 
be  multiplied  many  fold  and  the  time  required  for  transit  would  be  reducedtoa  minimum; 
because  the  intervals  between  cars  could  readily  be  made  as  small  as  one  minute,  requir- 
ing only  sufficient  time  to  unload  and  reload  the  foot  passengers  and  vehicles.  The 
car  should  be  made  double  deck,  the  pedestrians  being  carried  above;  and  the  roadway 
should  have  a  double  track,  the  right  one  being  for  the  use  of  a  single  street-car  and  the 
left  for  two,  or  possibly  three,  wagons.  At  the  end  of  the  trip  the  car  would  leave  first, 
and  the  wagons  would  follow  immediately,  edging  over  to  the  right  so  as  to  permit  of 
the  ingress  of  the  oncoming  car,  which  in  its  turn  would  be  followed  by  wagons  to  occupy 
the  left-hand  side.  While  the  vehicles  would  be  going  off  and  others  getting  on,  the 
upper  deck  could  easily  be  emptied  of  its  pedestrians  and  refilled. 

At  the  time  the  preceding  was  written  the  author  did  not  anticipate 
encountering  at  all  shortly  an  opportunity  to  figure  upon  a  transbordeur  of 
the  type  described;  but  in  1918  he  was  selected  by  the  City  of  New  Orleans 
as  bridge  expert  to  serve  as  one  of  the  three  members  of  the  Board  of 
Advisory  Engineers  specially  appointed  to  study  the  governing  conditions 
and  to  report  upon  the  advisability  of  bridging  or  tunneling  the  Missis- 
sippi River  at  or  near  that  city.  In  the  course  of  the  investigations,  which 
occupied  nearly  a  year,  there  arose  the  question  of  building  a  combined- 
highway-and-electric-railway  structure  connecting  New  Orleans  and 
Algiers.  As  the  line  joining  the  centers  of  gravity  of  these  two  places  is 
below  the  center  of  gravity  of  the  cities'  wharves,  many  ocean-going 
steamers  cross  it  daily,  and  there  will  be  a  still  greater  number  per  diem  in 
the  future.  For  this  reason  a  low-level  bridge  at  this  location  is  inadmis- 
sible, but  a  transbordeur  layout  would  undoubtedly  be  accepted  by  the 
War  Department,  as  the  resulting  structure  would  interfere  very  little, 
if  any,  with  navigation. 


320 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XXXII 


Through  the  courtesy  of  the  "Bridge  or  Tunnels  Committee"  of  the 
"PubHc  Belt  Railroad  Commission,"  the  author  is  permitted  to  utiUze  for 
this  memoir  the  results  of  the  transbordeur  investigations  which  he  made 
for  the  said  Board.  His  design  for  that  transbordeur  involved  multiple 
spans,  double  track,  multiple  cages,  and  rapid  transit,  the  speed  of  travel 
reaching  a  maximum  of  thirty  (30)  miles  per  hour.  Comparing  this  with 
the  before-mentioned  existing  single-span,  single-track,  single-cage,  slow- 
motion  structures,  it  is  evident  that  the  said  investigation  has  revolu- 
tionized transbordeur  designing  by  raising  the  carrying  capacity  per  hour 
to  something  like  that  of  the  corresponding  low-level  bridge,  when  due 
consideration  is  given  to  the  time  lost  by  reason  of  passing  vessels. 

In  the  New  Orleans  investigation  it  was  necessary  to  make  estimates  of 
cost,  based  on  ante-helium  unit  prices,  for  both  high-level  and  low-level 
combined-highway-and-street-railway  bridges,  notwithstanding  the  fact 
that,  in  all  probability,  the  latter  type  would  be  inadmissible;  and  estimates 
were  added  for  four  transbordeurs,  two  to  carry  cages  one  hundred  feet 
long  and  the  others  to  support  cages  of  half  that  length.  The  results  of 
these  computations  are  given  in  the  following  table: 


TABLE   32a 


Type  of  Structure 

Total  Cost  of  Structure 

Based  on  Ante-bellum 

Unit-Prices 

High-Level  Bridge 

Low-Level  Bridge 

Transbordeur  with  four  long  cages. .  .  . 

Transbordeur  with  six  long  cages 

Transbordeur  with  four  short  cages .  .  . 
Transbordeur  with  six  short  cages .... 

$5,590,000 
2,660,000 
3,160,000 
3,250,000 
2,450,000 
2,500,000 

From  the  preceding  table  may  be  drawn  the  following  conclusions: 

First.  The  high-level  bridge  is  more  than  twice  as  expensive  as  the 
low-level  bridge.  This  agrees  with  the  deductions  that  can  be  drawn  from 
comparisons  of  the  estimates  for  high-level  and  low-level  combined- 
bridges,  and  of  high-level  and  low-level  steam-railway  bridges,  which  were 
made  for  the  New  Orleans  investigation. 

Second.  The  transbordeur  with  short  cages  is  a  little  cheaper  than  the 
low-level  bridge. 

Third.  The  transbordeur  with  long  cages  is  some  22  per  cent  more 
expensive  than  the  low-level  bridge,  but  costs  only  58  per  cent  of  the  price 
of  the  high-level  bridge. 

The  utmost  capacity  of  the  transbordeur  with  six  short  cages  is  40  cages 
per  hour  in  each  direction;  and  each  cage  is  CMpablc  of  carrying  a  fully- 
loaded  street-car,  four  automobiles,  and  250  pedestrians,  making  40  cars. 


f  POSSIBILITIES    AND    ECONOMICS    OF    THE    TRANSBORDEUR      321 

160  automobiles,  .nd  10,000  pedestrians  per  hour  in  each  direction.  This 
estimate  is  based  upon  the  assumption  of  there  being  no  interference  from 
river  traffic.  Of  course,  the  capacity  of  the  transbordeur  with  six  long 
cages  is  about  twice  as  great  as  the  preceding  figures  indicate. 

Comparing  the  economics  of  the  transbordeur  with  short  cages  and 
that  with  cages  twice  as  long,  it  is  evident  that  the  addition  of  30  per  cent 
to  the  cost  of  the  former  will  nearly  double  its  transporting  capacity; 
consequently,  if  the  probable  demand  upon  the  structure  within,  say,  half 
a  century  be  greater  than  its  figured  capacity  for  short  cages,  it  might 
be  built  strong  enough  to  carry  long  cages,  and  be  operated  with  the 
short  ones  until  such  time  as  the  long  ones  are  required.  Moreover, 
it  would  be  practicable  to  connect  two  short  cages  so  as  to  form  the 
equivalent  of  one  long  one.  Such  an  arrangement  would  reduce  by 
about  $150,000  the  first  cost  of  the  most  expensive  of  the  four  trans- 
bordeurs  tabulated. 

As  for  the  question  whether  it  is  preferable  to  employ  four  or  six  cages — 
it  would  be  economical  to  adopt  four  at  first  and  then  increase  the  number 
to  five  and  finally  to  six  as  the  traffic  augments. 

It  should  be  noted  that  there  are  several  rather-widely-separated  cross- 
ings of  the  river  which  are  practicable  for  the  location  of  the  transbordeur, 
consequently  it  might  be  economic  to  build  the  cheaper  structure,  and  later, 
when  its  capacity  is  nearly  reached,  construct  another  some  distance 
away.  Two  widely-separated  structures  of  a  certain  capacity  would  be 
far  more  serviceable  to  the  public  than  a  single  structure  of  double  that 
capacity. 

The  transbordeur  may  prove  in  years  to  come  the  ideal  type  of  structure 
to  provide  for  pedestrian,  vehicular,  and  street-railway  traffic  across  the 
river  near  the  heart  of  the  City;  because  the  high-level  bridge  is  so  expen- 
sive and  involves  such  a  great  climb  and  such  long  detours  that  it  is  really 
out  of  the  question;  and  a  low-level  structure  below  the  up-stream  city- 
limits  would  offer  too  much  obstruction  to  navigation.  Owing  to  its  long 
spans  and  its  great  vertical  clearance,  which  extends  from  levee  to  levee, 
the  transbordeur  would  cause  less  obstruction  to  navigation  than  any 
other  possible  type  of  structure. 

While  the  cost  of  operating  a  transbordeur  may  figure  out  to  be  greater 
than  that  of  operating  the  movable  span  of  a  low-level  bridge  or  the  pas- 
senger elevators  of  a  high-level  bridge,  if  one  will  include  the  cost  of  the 
animal  power,  auto  power,  and  trolley  power  expended  in  traversing  a  low- 
level  bridge  (excluding,  of  course,  the  approaches),  the  economics  may  prove 
to  be  reversed. 

The  character  of  construction  and  the  modus  operandi  of  operation  of 
the  suggested  transbordeur  are  illustrated  in  Fig.  32a,  from  which  it  is 
seen  that  the  distance  between  centers  of  levees  at  the  selected  crossing  is 
2,250  feet,  divided  as  follows:   At  the  center  of  the  river  there  is  a  tower 


322  ECONOMICS   OF  BRIDGEWORK  Chapter  XXXII 

200  feet  long  transverse  to  the  stream;  and,  on  each  side  of  this,  a  700-foot 
span  with  a  cantilevered  end  extending  out  400  feet  beyond  a  supporting 
pier,  on  wliich  is  a  rocker-bent  that  is  stiffened  laterally  by  means  of  two 
fcriangular-braced  frames.  The  incKned  legs  thereof  connect  to  the  ends  of 
the  cantilever  arms  of  a  very  deep  steel-girder,  encased  in  concrete,  that 
joins  the  two  concrete  cyhnders  of  which  the  pier  is  composed.  There  is  a 
similar  arrangement  of  bracing  at  each  of  the  piers  near  mid-channel. 
The  outer  end  of  each  of  the  400-foot  spans  rests  on  a  roller  bearing  directly 
above  the  end  columns  of  a  steel-trestle  approach,  being  anchored  thereto 
so  as  to  prevent  any  upHft.  Of  course  there  can  be  no  bracing  in  the  cen- 
tral portion  of  any  one  of  the  braced  towers,  because  the  ferrj^  cars  or 
cages  have  to  pass  through  that  space.  The  trusses  are  100  feet  deep; 
and  they  are  braced  across  between  chords  in  both  horizontal  and  vertical 
planes,  so  as  to  stiffen  them  thoroughly.  The  long-type  cages,  of  which 
there  are  six,  are  about  100  feet  long  and  25  feet  wide  from  out  to  out. 
They  will  carry  on  one  side  of  their  lower  deck  a  Hne  of  track  long  enough 
for  two  street-cars,  and  alongside  of  these  there  will  be  space  for  five  or  six 
wagons,  or  eight  automobiles,  or  five  motor  trucks.  The  cage  is  to  be 
double-decked,  the  upper  deck  being  for  pedestrians  and  covered  with  a 
roof;  the  sides  are  to  be  open  to  permit  the  wind  to  blow  through,  but 
arrangement  must  be  made  to  cover  the  upper  portions  of  them,  occupied 
by  the  pedestrians,  in  case  of  rainy  or  cold  weather.  The  cages  are  sus- 
pended by  rigid  frames  braced  on  all  four  faces — completely  at  the  sides, 
and  at  the  ends  to  within  about  8  feet  of  the  top  of  the  upper  deck.  These 
cages  are  hung  by  trucks,  the  wheels  of  which  roll  on  rails  supported  by 
the  bottom  flanges  of  stringers.  In  order  to  avoid  delay,  the  cars  are  always 
to  be  suspended  from  overhead,  and  are  not  to  be  carried  by  tracks  on  the 
approaches  at  the  level  of  the  platform.  Near  the  outer  end  of  each 
trestle,  there  is  a  pair  of  independent  travelers  running  on  overhead  trans- 
verse tracks. 

At  each  end  of  the  structure  there  are  four  pockets,  two  for  operation 
and  two  for  storage.  The  latter  have  overhead  stringers  for  carrying  the 
wheels  of  the  traveling  cages. 

The  modus  operandi  is  as  follows : 

At  the  end  of  the  structure  shown  on  the  left  in  Fig.  32a,  a  traveling 
cage  comes  along  "Track  A"  and  passes  into  "Traveler  A,"  which  is 
immediately  moved  outward  into  "Pocket  A."  At  once  "Traveler  B" 
is  moved  so  as  to  face  "Track  A,"  from  which  it  receives  the  next  incoming 
cage,  and  then  moves  into  "Pocket  B."  Meanwhile  the  street  car,  the 
vehicles,  and  the  pedestrians  of  the  first  cage  have  passed  out  to  the  left, 
as  indicated  by  the  arrow,  and  the  cage  is  again  filled  by  a  car,  vehicles, 
and  pedestrians  coming  in  from  the  right,  as  shown  by  the  arrow  adjacent 
to  the  curved  center-line  of  street-railway  track.  Then  "Traveler  A" 
moves  over  to  face  "Track  B,"  and  the  cage  with  its  contents  starts  back 
across  the  structin-e,  immediately  after  wliich  "Traveler  A"  moves  over 


Fig.  32o.     Layout  of  Proposed  Transhordeur  for  Crossing  tile  Mississippi  Kiver  at  New  Orleans,  La. 


CB055  5£CT/0/^ 


To  Face  Page  Sll. 


POSSIBILITIES    AND    ECONOMICS    OF   THE    TRANSBORDEUR       323 

to  "Track  A"  to  receive  the  next  incoming  cage.  Then  "Traveler  B," 
its  cage  having  been  emptied  and  refilled,  as  indicated  by  the  arrows, 
passes  over  to  "Track  B,"  and  its  content  starts  back  across  the  structure. 
Finally  "  Traveler  B  "  moves  over  to  "  Track  A "  to  receive  another 
incoming  cage,  "Traveler  A"  having  meanwhile  received  an  incoming 
cage  and  moved  over  to  "Pocket  A."  This  completes  a  cycle  of  traveler 
operations  at  the  left  end. 

At  the  other  end,  the  first  returning  cage  enters  "Traveler  A',''  which 
immediately  moves  into  "Pocket  A',''  where  the  car,  vehicles,  and  pedes- 
trians pass  out  to  the  left,  as  indicated  by  the  arrow  adjacent  to  the  center- 
line  of  street-railway  track;  then  the  re-loading  is  done  from  the  right, 
as  indicated  by  the  other  arrow.  Meanwhile,  "Traveler  B'"  has  moved 
to  "Track  B,"  received  the  second  cage,  and  carried  it  to  "Pocket  B','' 
where  it  is  unloaded  to  the  left  and  reloaded  from  the  right,  as  shown  by 
the  arrows.  After  the  cage  in  "Traveler  A'"  is  reloaded,  the  said  traveler 
moves  over  to  "Track  A"  and  lets  the  cage  pass  out  for  another  trip. 
Then  "Traveler  A'"  moves  over  to  "Track  B"  to  receive  the  third  cage, 
which  it  takes  to  "Pocket  A',''  and  " Traveler  B'"  with  its  reloaded  cage 
passes  to  "Track  A"  to  discharge  its  contents.  This  completes  a  cycle 
of  traveler  operations  at  the  right  end. 

As  the  rush  traffic  of  the  morning  and  evening  hours  is  reduced,  one  or 
more  cages  can  be  run  to  the  storage  pockets,  where  they  can  be  lubricated, 
cleaned,  and  put  into  good  order;  and  at  night  a  single  cage  can  be  oper- 
ated by  filHng  all  four  of  the  storage  pockets  and  one  of  the  other  pockets 
with  cages. 

It  will  be  noticed  that  while  the  automobiles  and  the  other  vehicles 
always  head  in  the  same  direction,  they  do  not  have  to  back  out  of  the 
cages.  It  would  be  practicable  to  let  the  said  vehicles  head  in  either 
direction  by  putting  a  double  track  on  each  cage  and  turning  the  cars 
and  other  vehicles  out  quickly  to  the  right  on  the  approaches.  This 
would  necessitate  enclosing  in  a  "corral"  all  incoming  vehicles  until  the 
cage  is  emptied.  There  does  not  appear  to  be  much  choice  between  these 
two  methods  of  operation. 

Fig.  32a  indicates  the  method  of  caring  for  pedestrians.  They  pass  up 
the  stairways  shown  at  the  ends  to  covered  platforms  alongside  the  stor- 
age pockets,  where  they  await  the  arrival  of  the  cage;  and  they  would 
not  be  allowed  to  enter  the  latter  until  after  its  incoming  load  of  pedes- 
trians had  passed  off  by  the  adjacent  exit-stairway.  There  could,  there- 
fore, be  no  clashing  of  incoming  and  outgoing  pedestrians;  and  the  ap- 
proaches to  the  entering  stairway  could  be  arranged  so  as  to  avoid  any 
interference  between  the  pedestrians  and  vehicles  of  all  kinds. 

Assuming  a  maximum  attainable  velocity  of  thirty  miles  per  hour, 
which  may  not  always  have  to  be  utilized,  and  with  only  four  cages  and 
two  travelers  operating,  the  following  time  schedule  was  figured,  based 
upon  an  allowance  of  three  minutes  for  a  cage  to  cross  the  river: 


324 


ECONOMICS   OF   BRIDGEWORK 


Chapteb  xxxn 


Time  in 

Minutes 

Trav.  A 

Trav.  A' 

0 

Cage  1  enters  Trav.  A 

i 

Cage  1  enters  Pocket  A 

li 

Cage  1  leaves  Pocket  A 

2 

Cage  1  enters  Track  B 

2§ 

Cage  2  enters  Trav.  A 

2i 

Cage  2  enters  Pocket  A 

4i 

Cage  2  leaves  Pocket  A 

4i 

Cage  2  enters  Track  B 

5 

Cage  3  enters  Trav.  A 

Cage  1  enters  Trav.  A' 

7 

Cage  3  enters  Track  B 

Cage  1  enters  Track  A 

7J 

Cage  4  enters  Trav.  A 

Cage  2  enters  Trav.  A' 

9i 

Cage  4  enters  Track  B 

Cage  2  enters  Track  A 

10 

Cage  1  enters  Trav.  A 

Cage  3  enters  Trav.  A' 

12 

Cage  1  enters  Track  B 

Cage  3  enters  Track  A 

12 

Cage  2  enters  Trav.  A 

Cage  4  enters  Trav.  A' 

14J 

Cage  2  enters  Track  B 

Cage  4  enters  Track  A 

15 

Cage  3  enters  Trav.  A 

Cage  1  enters  Trav.  A' 

In  the  above  schedule  it  will  be  noted  that  during  the  first  four  and  a 
half  minutes  both  the  major  and  the  minor  operations  are  noted,  but  that 
in  the  next  ten  and  a  haK  minutes,  for  the  sake  of  brevity,  the  latter  are 
omitted. 

The  above  layout  gives  two-and-a-half  minute  service  in  each  direction. 

With  six  cages  and  four  travelers  operating,  the  following  time  schedule 
was  figured,  based  upon  an  allowance  of  two  and  a  quarter  minutes  for  a 
cage  to  cross  the  river: 


Time  in 

Minutes 

2J   Trav. 

3     Cage 

3i  Trav. 

3i 

3i 

4J 

4J 

4J   Trav. 

5  Trav. 
5i  Cage 
51  Trav. 

6  Cage 
6}  Trav. 
6i 

6i 
71 
7i 

7  J  Trav 

8  Trav, 
8}  Cage 
83  Trav 

9  Cage 


Time  in 
Minutes 

0 

0 
i 

u 

U 
U 

2 

2i 

Trav.  A 
A  faces  Trk.  A 
3  enters  Trav.  A 
A  enters  Pock.  A 


Trav.  A 
Trav.  A  faces  Track  A 
Cage  1  enters  Trav.  A 
Trav.  A  enters  Pocket  A 


Trav.  A  leaves  Pocket  A 
Trav.  A  faces  Track  B 
Cage  1  leaves  Trav.  A 


A  leaves  Pock.  A 

A  faces  Trk.  B 
3  leaves  Trav.  A 

A  faces  Trk.  A 
.5  enters  Trav.  A 

A  enters  Pock.  A 


A  leaves  Pock.  A 
A  fa^os  Trk.  B 

5  leaves  Trav.  A 
A  faces  Track  A 

1  cntera  Triiv.  A 


Trav.  B 


Trav.  B  leaves  Pock.  B 
Trav.  B  faces  Trk.  B 
Cage  2  leaves  Trav.  B 
Trav.  B  faces  Trk.  A 
Cage  4  enters  Trav.  B 
Trav.  B  enters  Pock.  B 


Trav.  B  leaves  Pock.  B 
Trav.  B  faces  Trk.  B 
Cage  4  leaves  Trav.  B 
Trav.  B  faces  Trk.  A 
Cage  G  enters  Trav.  B 
Trav.  B  enters  Pock.  A 


Trav.  A' 


Trav.  B  faces  Track  A 
Cage  2  enters  Trav.  B 
Trav.  B  enters  Pocket  B 


Trav.  A'  Trav.  B' 


Trav.  A'  faces  Trk.  B 
Cage  1  enters  Trav.  A' 
Trav.  A'  enters  Pock.  A' 


Trav.  B'  faces  Trk.  B 
Cage  2  enters  Trav.  B' 

Trav.  A'  leaves  Pock.  A'    Trav.  B'  enters  Pock.  B' 

Trnv.  A'  faces  Trk.  A 

Cage  1  leaves  Trav.  A' 

Trav.  A'  faces  Trk.  B 

Cage  3  enters  Trav.  A' 

Trav.  A'  enters  Pock,  A'    Trav.  B'  leaves  Pock  B' 
Trav.  B'  faces  Trk.  A 
Cage  2  leaves  Trav.  IV 


POSSIBILITIES    AND    ECONOMICS    OF    THE    TKANSBORDEUR      325 

This  layout  gives  one-and-a-half  minute  service  in  each  direction. 

The  preceding  method  of  handling  the  cages  by  means  of  travelers  was 
not  designed  instanter,  but  is  the  result  of  a  gradual  development  through 
a  series  of  tentative  studies.  The  first  idea  that  occurred  to  the  author 
was  to  carry  the  cages  by  the  suspension  system  around  a  loop  of  large 
diameter  at  each  end  of  the  route,  but  this  necessitated  a  very  awkward 
detail,  troublesome  to  operate,  consisting  of  a  pair  of  movable  platforms  to 
permit  cars  and  other  vehicles  to  enter  or  leave  the  cage  at  the  ends.  This 
alone  was  sufficient  reason  for  condemning  the  method;  but  there  was  a 
still-more-important  one,  viz.,  that  a  breakdown  of  one  of  the  traveling 
cages  would  tie  up  the  whole  line.  This  contingency  might  have  been 
provided  for  by  having  outside  of  each  loop  a  traveler  leading  to  a  "hos- 
pital" pocket;  but  that  detail  also  would  have  been  awkward  and  trouble- 
some to  operate,  hence  the  loop-system  project  was  soon  abandoned. 

Next  came  the  idea  of  using  switches  at  the  approaches,  but  it  was  evi- 
dent at  once  that  overhead  ones  were  impracticable  on  account  of  the 
necessity  for  cutting  through  the  supporting  girders,  hence  they  would 
have  to  be  located  beneath  the  cage,  which  would  then  require  trucks 
below  as  well  as  above,  and  the  support  would  have  to  be  changed  at  very 
short  intervals  between  the  upper  and  the  lower  systems.  This  method, 
too,  was  awkward,  requiring  both  time  and  an  additional  expenditure  of 
power  to  make  the  change,  consequently  it,  also,  was  soon  a,bandoned. 

Next  came  the  scheme  of  operating  the  two  tracks  as  entirely  inde- 
pendent units,  but  adjusting  the  times  for  starting  so  as  to  have  com- 
paratively regular  intervals  between  cages  in  each  direction.  This  scheme 
involved  the  idea  of  the  lateral  travelers  running  on  transverse  tracks 
below,  with  the  cage  still  supported  from  above  by  longitudinal  tracks 
which  would  be  a  continuation  of  those  on  the  span,  the  interval  between 
being  so  small  as  readily  to  be  jumped  by  the  wheels. 

The  layout  for  this  method  of  operation  is  shown  in  Fig.  326,  from  which 
it  is  seen  that  near  the  outer  end  of  each  trestle-approach  there  is  to  be  a 
pair  of  independent,  double-chambered  travelers  running  on  transverse 
tracks,  the  extreme  motion  of  each  traveler  being  about  25  feet.  These 
travelers  are  entirely  disconnected  from  the  top  of  the  trestle,  but  lie  up 
very  close  to  it.  Beyond  each  traveler  is  a  stationary  pocket  (large 
enough  to  receive  a  cage)  braced  at  the  sides,  but  open  at  the  river  end  for 
the  full  height,  and  open  at  the  shore  end  near  the  bottom  high  enough 
for  the  ingress  and  egress  of  vehicles  and  pedestrians. 

The  modus  operandi  is  as  follows:  As  shown  at  the  right-hand  side 
of  Fig.  326,  looking  from  the  river,  the  traveler  is  at  its  outer  position,  all 
three  of  the  cage-receptacles  being  vacant.  Cage  1  arrives  and  runs  into 
the  inner  chamber  of  the  traveler,  which  is  then  moved  inward  so  as  to 
allow  the  contents  of  the  cage  to  be  unloaded  and  a  new  load  to  be  taken 
on.  While  this  is  occurring,  Cage  2  arrives  and  passes  across  the  outer 
chamber  of  the  traveler  to  the  pocket  beyond,  and  from  there  the  unloading 


326 


ECONOMICS   OF   BKIDGEWORK 


Chapter  XXXII 


.OSZ  /^oqo  /aAPJi 

S/IP^  ao  A//CJ3//P/ 


POSSIBILITIES    AND    ECONOMICS    OF    THE    TRANSBORDEUR      327 

and  reloading  take  place.  Meanwhile  Cage  3  arrives  and  runs  into  the 
outer  chamber  of  the  traveler,  after  which  the  latter  is  moved  to  its  outer 
position,  so  as  to  allow  Cage  3  to  unload  and  reload.  This  brings  Cage  1 
into  position  to  begin  its  return  journey;  and,  after  the  proper  interval, 
Cage  2  also  starts  back.  Next,  when  Cage  3  is  loaded,  the  traveler  moves 
inward  so  as  to  permit  that  cage  to  start.  This  operation  is  repeated  at 
the  other  end  of  the  structure. 

The  operation  of  the  other  track  is  similar;  and,  as  previously  indicated, 
the  times  of  starting  the  two  groups  of  cages  are  adjusted  so  as  to  make  the 
intervals  between  all  cages  as  nearly  uniform  as  practicable. 

The  time  of  travel  was  figured  as  follows  for  the  round  trip  of  one  cage : 
Assuming  that  the  said  cage  is  in  its  pocket,  loaded  and  ready  to  start,  then 

Trip  across  structure  3,100  ft.  @  30  miles  per  hour  =  1.17  min. 

or,  to  allow  for  acceleration  and  retardation,  say 1.50  min. 

Wait  of  two  one-minute  intervals  between  cages,  which  time 
will  suffice  for  one  lateral  transfer  and  the  unloading  and  the 

reloading  of  the  cage 2.00  min. 

One  side  shift  of  traveler 0.25  min. 

Return  trip 1.50  min. 

Two  intervals  of  one  minute  each  between  cages 2.00  min. 

One  side  shift  of  traveler 0.25  min. 

Total  time  for  one  round  trip 7.50  min. 

The  number  of  round  trips  per  hour  for  each  cage  will  be  60-^7.5  =  8; 
and,  as  there  are  six  cages,  there  will  be  altogether  48  round  trips  made 
on  the  two  tracks. 

The  intervals  between  cages  on  each  track  in  the  same  direction  will  be 
one  min.,  one  min.,  and  five  and  a  half  min.  By  starting  the  first  cage  of 
the  group  of  three  on  Track  "B"  one  and  three-quarters  minutes  after  the 
third  cage  on  Track  "A"  has  left,  the  intervals  between  starts  at  either  end 
would  be  as  follows: 

1  min.,  1  min..  If  min.,  1  min.,  1  min.,  If  min.,  1  min., 
1  min.,  If  min.,  1  min.,  etc.,  etc., 

Under  the  assumption  of  cars  one  hundred  feet  long,  the  capacity  of  the 
structure  per  hour  in  each  direction  was  estimated  to  be  48,000  persons 
plus  a  large  but  .unknown  amount  of  freight.  Assuming  also  that  one- 
fourth  of  the  people  of  Algiers  would  go  to  New  Orleans  every  day,  and  that 
one-half  of  this  number  would  pass  over  in  a  space  of  three  consecutive 
hours,  this  structure  would  comfortably  accommodate  two  cities,  each 
having  a  population  of  a  milhon.  On  the  basis,  however,  of  the  accommo- 
dation of  passenger  automobiles  and  motor  trucks  in  the  proportion  of 
those  operating  in  the  City  of  New  Orleans,  viz.,  three  automobiles  to  each 
motor-truck  with  one  auto-vehicle  to  each  33  inhabitants,  and  assuming 


328  ECONOMICS   OF   BRIDGEWORK  Chapter  XXXII 

that  for  twelve  hours  per  day  the  cages  would  run  full  and  the  other  twelve 
hours  only  half  full,  the  proposed  transbordeur  would  serve  a  population  of 
about  475,000  in  Algiers,  or,  say,  400,000  to  allow  for  interruptions  from 
river  traffic.  Were  the  short  cages  used  instead  of  the  long  ones,  the  popu- 
lation that  could  be  served  would  be  200,000,  showing  that,  for  many  years 
to  come,  even  with  the  short  cages,  the  structure  would  have  ample  trans- 
porting capacity,  because  Algiers  at  present  is  only  a  small  community. 

The  next  improved  layout  is  shown  in  Fig.  32c,  which  indicates  that  the 
number  of  transverse  travelers  had  been  increased  to  six  and  that  the  travel 
on  each  track  is  in  one  direction  only.  In  this  case  the  travelers  run  on 
tracks  beneath  them;  but  after  the  drawing  had  been  made,  some  figuring 
showed  that  it  would  be  more  economical  to  suspend  the  said  travelers  from 
tracks  overhead,  as  indicated  in  the  layout  of  Fig.  32d.  In  both  of  these 
layouts,  by  using  only  four  cages,  one  traveler  at  each  end,  and  If  minutes 
for  crossing  the  river,  a  service  of  2f-minute  intervals  could  be  obtained, 
provided  there  were  no  interference  from  river  traffic.  With  three  travelers 
at  each  end  and  five  cages,  the  interval  would  be  reduced  to  2j  minutes; 
and  by  adding  another  cage  it  could  be  made  as  small  as  If  minutes.  As 
indicated  previously,  the  final  layout  with  only  two  travelers  at  each  end 
gave  2|-minute  intervals  with  four  cages  and  1^  minute  intervals  with  six 
cages,  thus  reducing  both  the  total  first  cost  and  the  expense  of  operation. 

It  is  difficult  to  compare  the  operating  capacity  of  a  transbordeur  with 
that  of  a  low-level  bridge  of  the  same  general  cross-section,  but  it  might  be 
well  to  make  the  attempt,  assuming  as  an  equivalent  low-level  structure  the 
layout  adopted  for  New  Orleans,  viz.,  the  author's  standard  city-bridge, 
having  a  clear  roadway  of  42  feet  with  two  street-railway  tracks  at  the 
middle  and  two  exterior  sidewalks,  each  of  eight  feet  clear  width. 

Assuming  three  lines  of  pedestrians  per  sidewalk  with  intervals  of  three 
feet  in  each  line,  which  represents  as  dense  a  crowd  as  could  cross  com- 
fortably, and  a  speed  of  three  miles  per  hour,  makes  15,840  foot-passengers 
per  hour  in  each  direction,  while  the  transbordeur  with  50  ft.-cages  could 
carry  about  two-thirds  of  that  number.  In  respect  to  a  combination  of 
street  cars  and  a,utomobiles,  the  average  speed  when  the  roadway  is  at  all 
crowded  will  not  exceed  twelve  miles  per  hour,  and  in  such  a  case  the  dis- 
tance between  autos  would  be  about  sixty  feet.  It  would  be  seldom  that 
there  would  average  more  than  one  street  car  per  minute  on  each  track,  and 
in  that  case  there  would  not  be  more  than  one  automobile  in  120  ft.  travel- 
ing along  the  street-car  space;  hence  there  would  be  1080+540=1620 
automobiles  passing  in  each  direction  per  hour  or  ten  times  as  many  as  the 
50  ft.-cages  would  carry.  There  would  be  about  one  and  a  half  times  as 
many  street-cars  traversing  the  bridge  as  could  be  carried  by  the  trans- 
bordeur with  the  short  cages.  Were  there  a  horse-drawn  vehicle  or  two  on 
one  side  of  the  roadway,  especially  a  heavily  loaded  one,  the  average  speed 
for  the  automol)iles  would  quiclvly  reduce  to  six  miles  per  hour  or  less, 
because  the  existence  of  occasional  street-cars,  as  well  as  the  automobiles 


POSSIBILITIES    AND    ECONOMICS    OF    THE    TRANSBORDEUR      329 


occupying  the  street-car  space,  would  prevent  the  other  automobiles  from 
passing  quickly  the  slow  vehicles.  This  cutting  of  the  speed  in  two  does 
not  by  any  means  halve  the  capacity  of  the  bridge,  but  it  certainly  reduces 
it  materially,  possibly  to  75  per  cent;  because  the  space  between  vehicles 
ould  reduce  with  the  decrease  in  velocity.     The  greater  the  number  of 


1030 


WO' 


iM^:. 


^-[^   s<^r>j    r>^ 


f leva  fed  P/afK>rm 
/or  Pedes/nan. 


■Pocke/B 


;^ 


73'-0'        m'O"      73'-0 


Fig.  32c,     Third  Preliminary  Study  for  Proposed  New  Orleans  Transbordeur. 
/O3'0''       //O'-O"       75'-0"      /OO'O'  .   Z^'o' 


45f.Py 


S/<7/nvay 


far /^^<ss/r/a/7s 


jw^- 


\Pocjl:e/Pi     ^ 


Fig.  32d.     Fourth  Preliminary  Study  for  Proposed  New  Orleans  Transbordeur. 

horse-drawn  vehicles  on  the  bridge  the  slower  would  be  the  average  speed 
of  the  procession  in  the  other  line;  and  with  a  great  many  of  them  on  the 
roadway,  the  automobiles  would  naturally  confine  their  travel  mainly  to  the 
street  car  line  and  adjust  their  speed  to  that  of  the  cars. 

It  is  evident,  therefore,  that,  before  designing  any  transbordeur,  one 
should  study  carefully  both  the  present  and  the  probable-future  proportions 
of  all  kinds  of  travel  and  adjust  the  design  upon  the  principle  of  "the 


330  ECONOMICS   OF  BKIDGEWORK  Chapter  XXXII 

greatest  good  for  the  greatest  number."  The  limitation  of  efficiency  will 
generally  be  found  to  be  the  capacity  for  transferring  automobiles;  and  this 
can  be  greatly  augmented  by  making  the  cages  three-decked,  taking  care 
of  the  street-cars  and  the  auto-trucks  on  the  lower  one,  the  automobiles 
on  the  middle  one,  and  the  pedestrians  above. 

From  the  preceding  reasoning  it  may  be  concluded  that  in  the  compari- 
son between  a  double-track  transbordeur  with  short-cages  and  a  standard, 
60  ft. -wide,  highway  bridge,  the  former  is  two-thirds  as  effective  for  both 
pedestrians  and  street-cars,  and  only  one-tenth  as  effective  for  automobiles. 
If  the  100  ft.-long  cages  were  used  and  only  one  street-car  were  carried  per 
cage,  the  rest  of  the  space  being  occupied  by  automobiles,  tho  preceding 
ratios  would  be  about  one  and  a  third,  two-thirds,  and  one-third;  or,  if  the 
long  cages  carried  two  street-cars  each,  these  figures  would  be  one  and  a 
third,  one  and  a  third,  and  one-fifth.  The  comparative  efficiencies  of  the 
two  structures  would,  consequently,  be  dependent  upon  how  the  traffic  is 
divided  between  pedestrians,  street  cars,  and  automobiles.  For  the  first 
two  the  transbordeur  can  readily  be  made  but  httle  lower  in  efficiency  than 
the  low -level  bridge,  but  for  auto-traffic  it  will  always  be  found  decidedly 
inferior;  and,  as  that  traffic  is  on  the  increase  in  both  amount  and  impor- 
tance, it  must  inevitably  be  concluded  that,  in  respect  to  general  carrying 
capacity,  the  transbordeur  is  never  as  satisfactory  as  the  said  low-level 
bridge. 

The  making  of  this  comparison  was  advisable,  although  by  no  means 
essential,  because  there  should  never  be  any  choice  between  a  bridge  and  a 
transbordeur  for  any  proposed  crossing.  As  stated  at  the  beginning  of 
this  chapter,  if  the  low-level  bridge  is  permissible,  it  should  be  adopted  ;. 
but,  if  not,  the  transbordeur  should  be  used  as  a  yis  oiler.  The  author's 
object  in  making  the  attempted  comparison  was  to  conffi-m  in  a  general 
way  his  a  priori  conclusion. 

As  previously  indicated,  there  will  not  be  many  occasions  for  the  build- 
ing of  the  transbordeur;  and  the  conditions  of  traffic,  navigation,  river- 
width,  and  property  for  approaches  are  so  variable  that  each  case  will 
require  a  thorough  and  systematic  compilation  of  them  all,  for  both  the 
immediate  and  the  distant  future,  and  an  exhaustive  study  of  the  question 
how  best  to  compromise  between  conflicting  interests  and  to  develop  in 
general  the  greatest  possible  efficiency. 

The  question  might  sometime  arise  as  to  whether  a  transbordeur  or  a 
high-level  bridge  would  be  preferable  for  the  crossing  of  a  waterway  navi- 
gated only  by  river  steamers,  for  which  the  Government's  clearance-require- 
ment generally  varies  from  50  to  60  feet  above  high-water  elevation;  con- 
sequently, it  would  be  well  to  know  in  advance  the  approximate  ratios  of 
cost  of  a  transbordeur  to  the  various  costs  of  the  corresponding  high-level 
bridges  having  differing  vertical  clearances.  For  this  purpose  Fig.  32e 
was  prepared  by  using  as  a  basis  a  slight  modification  of  some  of  the  results 
of  the  computations  for  the  New  Orleans  Bridge  study.     That  figure  gives 


POSSIBILITIES    AND    ECONOMICS    OP    THE    TRANSBORDEUR      331 


for  the  crossing  at  that  place,  when  the  pier-locations  and  span-lengths  are 
constant,  the  ratios  of  costs  of  fixed-span  bridges  and  their  approaches  for 
all  clearances  above  high  water  up  to  200  feet,  using  as  the  comparing  unit 
the  cost  of  the  bridge  having  a  clearance  of  only  ten  feet,  which  is  as  small 
as  generally  is  permissible.  Curiously  enough,  the  costs  of  the  three 
bridges  specially  figured  for  the  diagram  make  the  record  a  straight  line. 
The  cost  of  the  transbordeur  with  short  cages  in  this  case  is  almost  equal  to 
that  for  a  fixed-span  bridge  having  a  clearance  of  ten  feet,  as  given  by  the 
diagram;  and  that  for  a  clearance  of  60  feet  is  shown  to  be  1 . 28  times  that 
for  the  lowest  structure  and,  therefore,  also  1.28  times  that  for  the  trans- 
bordeur. In  view  of  the  comparatively  small  difference  in  cost  between 
0         20         40         60         80         100        W         140        160        130      200) 


Fig.  32e. 


iO  40         60         dO         m         120         140         160 

Ver/ica/  Cfecrance  adove  ///^/>  Wder  /n  Fesf 

Ratios  of  Costs  of  Fixed-Span  Bridges  and  their  Approaches  for  Various 
Clearances  Above  High  Water. 


transbordeur  and  fixed-span  bridge,  and  of  the  facts  that  a  climb  of  65  feet 
above  the  water  is  by  no  means  prohibitory  for  any  class  of  vehicle,  even 
the  horse-drawn, — that  the  carrying  capacity  of  the  bridge  is  generally 
greater  than  that  of  the  transbordeur  for  both  pedestrians  and  street-cars 
and  always  much  greater  for  automobiles, — and  that  horse-drawn  vehicles 
are  fast  becoming  obsolete, — the  deduction  may  be  made  that,  for  crossings 
with  moderately-high  vertical-clearance,  the  fixed-span  bridge  is  decidedly 
preferable  to  the  transbordeur.  It  is  true  that  this  general  inference  has 
been  drawn  from  a  single  case,  and  on  that  account  may  not  be  satis- 
factory to  some  engineers;  but  the  author  is  of  the  opinion  that,  were 
similar  reasoning  applied  to  any  other  practical  case,  a  like  conclusion  would 
be  reached. 


332  '        ECONOMICS  OF  BEIDGEWORK;  Chapter  XXXII 

Before  closing  this  chapter  the  author  has  decided  that  it  will  be  well  to 
take  two  pending  cases  from  his  own  practice  and  indicate  how  they  should 
be  solved.  One  is  that  of  the  crossing  of  Havana  Harbor,  Cuba,  so  as  to 
develop  a  tract  of  beautifully-situated  and  almost-entirely  unoccupied 
land  about  five  miles  long  and  one  mile  wide  parallehng  the  coast  line. 
Some  seven  years  ago  the  author  spent  considerable  time  and  money  on  the 
development  of  the  project  to  build  a  high-level,  cantilever,  highway-and- 
street-railway  bridge  over  the  entrance  channel  near  the  inner  end  of 
Cabana  Castle  at  a  location  quite  close  to  the  place  where  the  said  channel 
expands  into  the  body  of  the  gourd-shaped  bay  forming  the  anchorage- 
ground  of  the  harbor.  Just  as  the  project  was  about  to  materialize,  the 
war  in  Europe  began;'  and  ever  since  then  it  has  been  impracticable  to 
raise  money  for  any  large  enterprise  not  directly  connected  with  war  work. 
However,  the  time  is  probably  close  at  hand  when  it  will  be  advisable  to 
try  to  revive  the  scheme,  because  sooner  or  later  a  bridge  of  some  kind  will 
certainly  be  built  across  the  channel  so  as  to  permit  the  city  to  expand  in 
the  one  possible  direction  that  will  permit  of  the  building  of  fine  residences 
within  quick  reach  of  the  business  center.  The  old  layout,  shown  in  Fig. 
32/,  necessitated  the  carrying  of  all  traffic  from  an  elevation  of  five  feet 
above  water  level  on  the  city  side  by  means  of  a  spiral  approach  and 
passenger  elevators  to  an  elevation  of  two  hundred  and  four  feet  above 
the  same,  and  then  down  to  an  elevation  of  about  one  hundred  and  fifty 
feet  at  the  entrance  to  the  North  approach. 

About  a  year  ago,  it  struck  the  author  that  it  might  be  better  to  build  a 
double-track  transbordeur  quite  close  to  the  mouth  of  the  harbor  and  to 
carry  the  traffic  across  at  an  elevation  of  about  eighty  feet  above  the  water. 
Near  La  Punta,  the  outermost  land  on  the  City  side  of  the  channel,  there  is 
a  large  area  of  open  ground  which  rises  gradually  to  an  elevation  of  twenty- 
five  or  thirty  feet  some  four  or  five  blocks  back  from  the  water;  and  at  the 
other  side  of  the  harbor,  between  Morro  and  Cabana  Castles,  the  elevation 
of  the  land  is  much  lower  than  it  is  farther  in.  By  starting  with  a  trestle 
approach  near  the  South  end  of  the  said  open  ground  and  rising  on  a  four 
per  cent  grade,  more  or  less,  to  within  about  five  hundred  feet  of  mid-chan- 
nel, it  would  be  practicable  to  attain  the  elevation  just  mentioned  for  the 
cage  deck;  and  on  the  other  side  a  short  trestle  with  an  easy  up-grade 
would  lead  to  the  general  surface  of  the  ground  back  of  the  two  castles. 
The  length  of  span  over  the  channel  would  not  be  more  than  800  feet;  and, 
possibly,  it  might  be  a  hundred  feet  shorter,  thus  making  the  travel  of  the 
cages  only  800  or  900  feet.  On  that  account  it  would  not  be  economical 
to  adopt  the  transverse  travelers,  because  the  time  required  for  crossing  is 
so  short.  It  would  pay  better  to  widen  the  structure  and  put  in  another 
track  or  two,  should  the  prospective  traffic  warrant  it,  especially  as,  on 
account  of  the  great  height  of  the  overhead  span,  a  large  width  of  structure 
is  necessary  for  resisting  properly  the  overturning  effect  of  the  wind  pres- 
sure, which  during  tropical  storms  is  likely  to  be  excessive.     In  order  to 


POSSIBILITIES    AND    ECONOMICS    OF    THE    TRANSBORDEUE      333 


334  ECONOMICS   OF   BRIDGEWORK  Chapter  XXXII 

secure  a  large  capacity,  it  would  be  advisable  to  make  the  cages  three- 
decked,  and  possibly  longer  than  fifty  feet.  Again,  ui  order  to  save  tune  in 
unloading  and  reloading,  the  street-cars  leaving  the  city  side  could  take  the 
lower  deck  and  the  automobiles  and  other  vehicles  leaving  the  same  could 
occupy  the  middle  deck,  the  pedestrians,  of  course,  always  using  the  upper 
deck.  Starting  from  the  other  side,  the  automobiles  could  occupy  the  lower 
deck,  and  the  street-cars  the  middle  deck.  By  this  arrangement  the  climb- 
ing of  the  comparatively  steep  grade  at  the  North  end  from  the  lower-deck 
level  would  be  done  by  street-cars  only,  and  time  would  be  saved  by  holding 
the  automobiles  and  horse-drawn  vehicles  in  a  corral  until  after  the  street- 
car has  left  clear  both  the  cage  and  the  portion  of  the  approach  close  thereto. 
Similarly,  the  street-car  would  be  held  in  a  corral  until  after  aU  the  other 
vehicles  have  gotten  out  of  the  way.  Barring  interference  from  navigation, 
each  cage  could  make  a  round  trip  in  about  3|  minutes,  which  would  give 
17  round  trips  per  hour,  or  34  trips  per  hour  in  each  direction  by  the  two 
cages.  A  60  ft. -cage  would  carry  two  street-cars,  eight  auto-vehicles,  and 
300  pedestrians,  making  68  cars,  272  auto-vehicles,  and  10,200  pedestrians 
per  hour  in  each  direction.  Allowing  for  interruptions  from  navigation, 
which  would  not  be  serious,  because  of  the  great  clearance  beneath  the 
cages  that  would  permit  a  large  proportion  of  passing  craft  to  go  by  with- 
out stopping  operation,  it  would  be  legitimate  to  count  upon  a  maximum 
limit  of  60  street-cars,  240  automobiles,  and  9,000  pedestrians  per  hour  in 
each  direction.  Deducting  liberally  for  service  to  outlying  towns,  the 
remaining  capacity  would  be  great  enough  to  provide  for  a  population  of 
at  least  75,000  persons,  or  15,000  per  square  mile,  which  is  fairly  dense  for 
a  residence  district. 

Fig.  32gr  shows  in  skeleton  outline  the  elevation  of  this  transbordeur 
span  with  a  short  portion  of  each  of  the  adjacent  approaches,  also  a  cross- 
section  of  the  structure  at  mid-span.  From  this  drawing  it  will  be  seen 
that,  in  reality,  there  are  two  distinct,  parallel,  cantilever  bridges  located 
a  short  distance  apart  and  connected  to  each  other  by  cross-girders  and 
bracing,  leaving  ample  space  between  for  the  safe  passage  of  the  two  cages; 
that  the  latter  pass  shoreward  beyond  each  main  pier  a  distance  equal  to 
one  panel-length  of  the  anchor  arm,  connecting  to  an  approach  deck  that 
is  suspended  from  the  other  two  panel  points  of  the  said  anchor  arm;  that 
all  the  panels  of  the  entire  structure  are  of  equal  length,  there  being  three 
of  the  n  in  each  anchor  arm,  five  in  each  cantilever  arm,  and  six  in  the  sus- 
pended span;  and  that  the  outlines  of  all  chords  are  parabolic  curves. 
Each  main  pier  consists  of  four  pneun^atic  cylinders  sunk  to  bed  rock,  each 
cylinder  being  surmounted  by  a  truncated  concrete  cone,  and  the  three 
spaces  between  the  four  cones  being  filled  with  thin,  reinforced-concrete 
walls.  Each  anchor-pier  shaft  consists  of  a  mass  of  concrete  supported 
upon  a  coiicreto  liase  that  rests  on  piles.  Tho  niithor  believes  that  the 
bold,  (Mirved  oiitlinos  of  the  tniss(^s,  in  spite  of  tlio  liorizontal  line  of  girders 
between  the  twin  spans,  would  make  an  a^stlietic  structure  that  would  be 


fieVdT/ON  _ 

Sca/e    /'=SO'o' 
Fig.  32j?.     General  Layout  fur  a  Prupust-d  Traiisljordcur  to  Cruss  Havana  Harbor,  Cuba. 


3ECTioNffT  Af/D-cmmn 

To  face  page  3S4- 


POSSIBILITIES    AND    ECONOMICS    OF   THE    TRANSBORDEUR      335 

in  keeping  with  the  cominantling  position  which  it  would  occupy  at  the 
entrance  to  one  of  the  most  beautiful  harbors  in  the  world. 

The  other  case,  as  indicated  at  the  beginning  of  this  chapter,  is  that  of  a 
proposed  suspension  bridge,  having  a  single  span  of  1,750  feet  which 
clears  the  entire  width  of  river  between  the  established  harbor  lines,  to 
join  the  cities  of  Philadelphia  and  Camden. 

Quite  lately  the  author  was  struck  with  the  idea  that  a  transbordeur 
might  serve  all  the  traffic  at  the  crossing  and  save  considerable  money 
as  compared  with  a  bridge,  consequently  he  had  his  office  prepare  a  layout, 
using  a  three-deck  cage  to  carry  street-cars,  automobiles,  and  pedestrians; 
but  a  short  preliminary  economic  study  showed  that  the  expense  involved 
would  be  too  great,  consequently  he  prepared  a  two-deck  layout  that  does 
not  carry  street-cars.  These  would  run  around  a  loop  on  each  approach 
and  would  discharge  and  take  on  passengers  close  to  the  loading  places  of 
the  cages.  An  estimate  of  cost  was  made  for  this  layout  based  on  the  then- 
ruling  prices  of  materials  and  labor,  the  grand  total,  excluding  right-of-way, 
property  damages,  and  interest  during  construction,  amounting  to  $12,- 
000,000.  Then  a  layout  was  made  for  a  bridge  and  its  approaches,  and  a 
similar  estimate  of  cost  was  prepared,  amounting  to  $13,400,000. 

As  these  two  amounts  differ  so  little,  it  was  at  once  concluded  that  for 
this  crossing  there  would  be  no  real  economy  in  adopting  a  transbordeur. 
The  ratio  of  the  said  amounts  is  about  0.9,  while  the  corresponding  ratio 
for  the  New  Orleans  study  was  only  0.58. 

From  these  figures  it  may  be  concluded  that  a  long-span-suspension 
layout  does  not  accommodate  itself  to  the  carrying  of  transbordeur  cages 
as  economically  as  does  a  layout  of  several  shorter  continuous  spans. 
The  explanation  of  this  fact  is  that  the  piers  for  the  two  cases  are  about 
alike,  that  the  approaches  of  the  transbordeur  are  nearly  but  not  quite  as 
expensive  as  those  of  the  bridge,  and  that  while  there  is  a  large  saving  in 
the  combined  costs  of  superstructure  and  anchorages,  it  is  largely  offset 
by  the  cost  of  the  cages,  travelers,  and  pockets.  In  the  New  Orleans 
investigation  the  substructure  of  the  transbordeyr  would  cost  but  little 
more  than  one-half  of  that  for  the  corresponding  bridge,  and  the  cost  of 
the  approaches  to  the  former  is  a  bagatelle  when  compared  with  that  of 
those  to  the  latter;  but  the  total  steelwork  for  the  river  spans,  towers, 
bents,  cages,  travelers,  and  pockets  of  the  transbordeur  exceeds  in  value 
that  of  the  river  spans  of  the  bridge. 

Conclusion  and  Recapitulation 

The  title  of  this  chapter  indicates  that  it  is  intended  to  show  both  the 
possibilities  and  the  economics  of  what  in  slang  parlance  might  be  termed 
the  ''glorified"  transbordeur,  i.e.,  the  existing  type  of  transporter  bridge 
expanded  and  enlarged  many  fold  so  as  to  accommodate  it  to  wide  rivers, 
high  carrying  capacity,  and  rapid  transit.     Some  of  its  possibilities  have 


336  ECONOMICS   OF   BRIDGEV/ORK  Chapter  XXXII 

been  shown,  but  probably  not  all  of  them;  and  as  for  the  economics,  it 
has  been  proved  to  cost  less,  even  in  extreme  cases,  than  a  very-high-level 
structure,  and  about  the  same  as  a  low-level  structure;  but  that,  strictly 
speaking,  it  cannot  be  said  to  be  in  economic  competition  with  either 
type;  because  when  the  conditions  really  call  for  the  consideration  of  a 
transbordeur,  a  very-high-level  bridge  would  generally  necessitate  too 
great  a  climb  for  the  traffic,  and  a  low-level  bridge  would  be  barred  because 
of  its  interfering  too  much  with  the  paramount  interest  of  navigation. 
.The  Philadelphia-Camden  case  is  apparently  an  exception  to  this  rule, 
but  it  must  be  remembered  that  its  vertical  clearance  is  only  135  feet, 
while  that  for  the  proposed  crossing  at  New  Orleans  is  175  feet,  and  that 
the  extra  forty  feet  of  height  make  a  great  difference  in  the  costs  of  the 
approaches. 


CHAPTER  XXXIII 


ECONOMICS    IN    CONTRACT-LETTING 


At  first  thought  one  might  be  incHned  to  claim  that  contract-letting  is 
not  a  matter  of  economics,  but  a  little  reflection  will  soon  convince  him 
that  it  certainly  is,  because  if  contracts  be  badly  drawn,  or  if  the  modus 
operandi  of  compensating  the  contractor  and  his  workmen  be  faulty,  the 
work  of  construction  will  assuredly  cost  more  than  it  would  under  ideally 
perfect  conditions.  During  the  last  few  months  the  author  has  been 
writing  a  series  of  papers  on  contract-letting  and  profit-sharing,  culminating 
in  a  lengthy  discussion  of  a  paper  by  Mr.  Ernest  Wilder  Clarke,  published 
in  the  August,  1919,  Proceedings  of  the  American  Society  of  Civil  Engineers, 
the  said  discussion  appearing  in  the  October-November-December  Pro- 
ceedings. 

As  this  discussion  is  in  reality  a  complete  treatment  of  the  subject,  and 
was  intended  as  such  (although  for  good  and  sufficient  reasons  presented 
as  an  adjunct  to  another  paper  instead  of  being  offered  as  a  separate 
memoir),  it  is  here  reproduced  practically  verbatim. 

The  importance  of  the  subject  of  this  paper,  to  owners,  contractors,  and 
the  entire  American  nation,  cannot  well  be  exaggerated;  for,  until  there  is 
reached  a  satisfactory  compromise  between  owners  on  the  one  hand  and 
contractors  on  the  other  concerning  the  vital  questions  of  contract-letting 
and  profit-sharing,  the  business  of  the  country  will  fail  to  recuperate  to 
the  extent  that  it  should  at  this  critical  period  in  the  readjustment  of  all 
constructional  activities — which  activities  were  so  fundamentally  upset 
throughout  the  whole  world  more  than  five  years  ago  by  the  advent  of  the 
World  War.  The  opportunity  now  within  easy  reach  of  the  American 
people  to  secure  the  bulk  of  the  world's  trade  is  unique;  but,  apparently, 
our  leaders  in  diplomacy,  manufacture,  shipping,  business,  and  finance 
are  either  unaware  ot  its  existence  or  indifferent  about  taking  advantage 
of  their  good  fortune.  The  Latin-American  nations  are  now  knocking 
at  our  door  asking  to  do  business  with  us  and  begging  us  to  lend  them 
money  for  the  development  of  their  as-yet-almost-virgin  lands,  mines,  and 
water  powers,  and  their  other  more  or  less  embryonic  resources;  and  the 
leading  peoples  of  Asia,  Africa,  Australasia,  and  even  Europe  are  to-day 
much  more  willing  to  enter  into  business  relations  with  this  country  than 
they  have  ever  been  before.  They  all  recognize  that,  for  the  present  at 
least,  the  European  countries  are  in  no  condition  to  lend  money,  being 

337 


338  ECONOMICS   OF   BRIDGEWORK  Chaptek  XXXIII 

themselves  borrowers  and  having  so  many  demands  at  home  for  their 
time,  attention,  and  capital  that  they  are  unable  to  give  consideration  to 
the  needs  of  any  nation  but  their  own;  and  the  entire  civihzed  world  is 
well  aware  of  the  fact  that,  in  spite  of  our  vast  war  debt,  we  are  today  the 
most  wealthy  of  all  peoples. 

These  conditions — unfortunately,  as  far  as  we  are  concerned — will 
not  last  indefinitely;  and  if  we  are  so  short-sighted  as  to  neglect  to  seize 
the  golden  opportunity  which  is  not  only  easily  within  our  reach,  but  which 
is  actually  being  tendered  to  us  and  almost  forced  on  our  acceptance,  it  will 
not  be  long  before  both  England  and  Germany  will  re-secure  the  grip  on 
the  world's  trade  which  they  possessed  in  ante-bellum  days. 

Prevention  of  Progress.  One  of  the  greatest  stumbhng  blocks  in  the 
pathway  of  our  nation's  advancement  is  the  conflict  between  labor  and 
capital;  and  until  it  is  removed  the  wheels  of  progress  will  be  clogged,  and 
the  present  paralyzation  of  all  great  peace  industries  will  continue  to  exist — 
possibly  in  even  worse  form  than  it  does  today.  Again,  the  main  issues 
between  labor  and  capital  are  these  questions  of  contract-letting  and  profit- 
sharing.  If  they  were  once  settled  to  the  satisfaction  of  all  concerned — 
bankers,  manufacturers,  contractors,  and  workmen — all  other  minor  dif- 
ferences would  quickly  be  adjusted.  Such  a  settlement  is  perfectly 
feasible;  and  the  possibility  of  its  speedy  accomphshment  is  neither  a 
Utopian  conception  nor  an  idle  dream. 

Primarily,  the  men  who  do  the  work  must  have  a  substantial  share 
in  all  net  profits  of  manufacture  and  construction;  but  the  way  for  them 
to  obtain  it  is  not  by  the  organization  of  strikes  nor  by  seizing  the  plant 
and  running  the  business  of  the  manufacturer  or  the  contractor.  The 
uneducated  workman  is  no  more  fit  to  manage  business  and  to  handle 
industry  than  the  sedentary  office  man  is  to  undertake  the  physical  labor 
of  the  workman — in  fact,  much  less  so;  because  it  would  generally  be 
totally  impracticable  to  educate  the  illiterate  workman  up  to  a  state  of 
efficiency  which  would  enable  him  to  undertake  business  management 
and  finance,  while,  in  most  cases,  in  a  comparatively  short  time,  the  office 
man's  muscles  could  be  developed  sufficiently  to  enable  him  to  endure  the 
physical  stress  of  the  workman's  job.  Nothing  of  value  can  be  accom- 
plished by  mob  rule,  as  the  pending  subsidence  of  the  present  wave  of 
Bolshevism  will  soon  prove. 

Labor  and  Capital.  Although  it  is  certainly  true  that  the  laborer 
cannot  succeed  independently  of  the  business  man,  it  is  equally  true  that 
the  lattci'  cannot  accomplish  much  without  the  aid  of  the  capitalist,  hence 
it  behooves  business  men  and  financiers  to  f^ome  quickly  to  a  friendly  under- 
standing and  agreement.  In  times  past,  the  capitalist  secured  and  exer- 
cised a  strangle  hold  on  the  promoter,  the  manufacturer,  and  the  con- 
tractor, often  forcing  them  to  turn  over  the  lion's  share  of  their  profits 
as  compensation  for  the  use  of.  money  in  the  development  of  their  under- 
takings;   and  these  men  in  their  turn  endeavored  to  even  up  matters  by 


ECONOMICS   IN   CONTRACT   LETTING  339 

getting  their  pound  of  flesh  out  of  the  workman  by  compeHing  him  to 
labor  long  hours  for  meager  compensation.  Today,  the  laboring  man  is 
beginning  to  come  into  his  own;  but  if  he  unwisely  takes  too  great  advan- 
tage of  his  growing  power,  he  will  "kill  the  goose  that  lays  the  golden  eggs," 
and  this  will  ruin  his  chance  of  securing  comfort  and  happiness  for  himself 
and  his  family. 

The  first  step  requisite  for  quieting  the  existing  widely  spread  popular 
unrest  and  returning  to  normally  prosperous  conditions  is  to  bring  together, 
so  that  they  may  operate  in  harmony,  the  financier,  the  employer,  and  the 
laborer;  and  this  must  be  accomphshed  primarily  by  establishing  some 
method  of  contract-letting  and  profit-sharing  which  will  be  just  and 
equitable  to  all  parties  interested.  For  some  time,  the  author  has  been 
endeavoring  to  formulate  and  develop,  through  communications  to  the 
technical  press,  an  ideal  method  of  accomplishing  this  desideratum;  and 
later  herein  he  will  indicate  clearly  of  what  it  consists.  First,  however,  he 
will  discuss  in  detail  not  only  the  suggestions  offered  by  Mr.  Clarke  in  his 
timely  paper,  but  also  those  of  various  engineers  and  political  economists 
who  have  of  late  been  treating  the  matter  in  print. 

Various  Methods  of  Contract-Letting.  The  common  ways  of  contract- 
letting  are  the  following: 

A.  Lump  smn  for  complete  construction. 

B.  Schedule  rates  for  all  materials  in  place. 

C.  Actual  cost  plus  a  percentage,  with  some  kind  of  allowance  for 
overhead  expenses. 

D.  Actual  cost  of  labor  and  materials  plus  a  percentage,  with  no 
allowance  for  overhead  expenses. 

E.  Actual  cost  plus  a  lump  sum,  with  some  kind  of  allowance  for  over- 
head expenses. 

F.  Actual  cost  of  labor  and  materials  plus  a  lump  sum,  with  no  allow- 
ance for  overhead  expenses. 

G.  Actual  cost  plus  a  profit  based  on  small  unit  prices  agreed  upon  in 
the  contract,  as  advocated  of  late  by  Mr.  G.  H.  Hailey. 

H.  Various  methods  of  profit  sharing  between  the  client  and  the 
contractor. 

Method  A  generally  appeals  best  of  all  to  the  client,  because  it  fixes  in 
advance  what  the  construction  is  going  to  cost  him,  unless,  perchance, 
there  are  important  variations  in  the  estimated  total  quantities  of  materials, 
due  to  lack  of  sufficient  preliminary  information  or  to  the  encountering  of 
conditions  that  could  not  well  have  been  foreseen.  It  is  by  no  means  as 
satisfactory  to  the  contractor,  however,  who  has  to  run  the  risk  of  being 
actually  out  of  pocket  on  the  job,  in  addition  to  the  loss  of  personal  time 
and  effort. 

Method  B  is  quite  an  improvement  on  Method  A,  in  that  the  contractor 
does  not  have  to  guarantee  the  correctness  of  the  estimated  quantities  of 
materials;  but  the  prime  objection  to  Method  A  holds  good  for  Method  B, 


340  ECONOMICS   OF   BRIDGEWORK  Chapter  XXXIII 

as  the  latter  does  not  prevent  the  contractor  from  losing  monej-  heavily 
on  the  venture. 

In  the  days  of  hard  times,  when  contractors  are  wilhng  to  take  work 
at  low  figures,  and  even  below  cost,  in  order  to  keep  their  force  together, 
the  public,  in  general,  especially  as  represented  by  companies  and  munici- 
palities, is  prone  to  take  advantage  of  them  by  insisting  that  work  be  let 
by  the  lump  sum,  and  by  throv\^ing  on  the  unfortunate  "successful  biddpr" 
not  only  the  risk  of  loss  from  rising  prices  of  materials  and  labor  and  from 
unforeseen  contingencies,  but,  also,  in  many  cases,  from  excess  of  quan- 
tities above  those  given  in  the  specifications.  This  is  accomplished  by 
inserting  in  the  latter  a  most  unjust  clause  compelling  each  bidi.!er  to  verify 
for  himself  both  the  quantities  stated  and  the  character  of  the  conditions 
described.  The  bidders,  hungry  for  work,  accept  this  clause  without 
comment,  but  with  the  mental  reservation  that,  in  case  of  hard  luck,  they 
will,  by  some  means  or  other,  obtain  extra  compensation,  even  if  they 
have  to  carry  the  controversy  into  the  Courts. 

In  nineteen  cases  out  of  twenty,  it  is  unjust  to  bidders  to  ask  them  to 
name  a  lump-sum  compensation  for  doing  work,  unless  provision  is  made 
for  a  variation  in  the  quantities  of  materials  on  which  they  tender.  If 
provision  is  arranged  for  such  variation,  the  method  of  letting  is  no  longer 
that  of  the  "lump  sum,"  but  reduces  to  a  modification  of  that  of  "unit 
prices." 

As  before  indicated,  the  latter  method  is  certainly  the  more  logical, 
and  yet  it  is  far  from  being  entirely  fair  to  the  contractor;  because,  although 
it  provides  against  loss  through  excess  above  the  estimated  quantities  of 
materials,  it  leaves  him  open  to  the  possibility  of  still  greater  loss  through 
changing  prices,  onerous  unanticipated  conditions,  and  disastrous  hap- 
penings beyond  his  control.  Up  to  a  certain  point,  the  client  is  the  proper 
party  to  assume  the  principal  risks  inherent  to  the  work,  provided  that  the 
adverse  happenings  are  really  unavoidable  by  the  contractor,  and  that 
the  latter  takes  every  reasonable  precaution  against  disaster  or  loss.  And 
yet  the  contractor  should  not  be  altogether  relieved  from  the  possibility 
of  loss  due  to  hard  luck,  because  such  misfortune  is  often  caused  by  his 
dilatoriness,  which  carries  the  work  into  an  unfavora])le  season  for  field 
operations.  The  idea,  promulgated  of  late  by  certain  writers,  that  it  is 
unjust  ever  to  penalize  a  contractor,  is  wrong;  because  he,  like  eveiybody 
else  in  this  world,  should  bear  the  burden  resulting  from  his  own  careless- 
ness, negligence,  or  incompetence.  The  owner  surely  has  some  rights — 
and  this  is  one  of  them.  A  liberal  limit  of  total  cost  which  can  be  increased 
or  reduced  properly,  in  order  to  provide  for  an  increase  or  decrease  in  the 
estimated  total  quantities  of  materials,  will  prevent  the  owner  from  being 
excessively  overcharged,  and  still  will  give  the  contractor  every  oppor- 
tunity to  come  out  whole  in  any  case  except  that  of  extraordinary  hard  luck. 

M(ithod  C  is  wholly  objectionable  to  the  client,  in  that  it  places  him 
entirely  at  the   mercy  of  the   contractor  and  his  men.     The  allowanc 


ECONOMICS   IN   CONTRACT   LETTING  341 

for  overhead  may  be  either  an  assumed  percentage,  or  the  actually  com- 
puted amount  in  complete  detail,  the  former  being  generally  the  less  objec- 
tionable. Even  if  the  contractor  is  perfectly  honest  and  has  the  best  will 
in  the  world  to  keep  down  the  cost  for  the  benefit  of  the  client,  his  employees 
will  not  have  that  desire.  In  effect,  they  say  to  themselves  and  to  each 
other,  "What  is  the  use  in  my  exerting  myself  unduly?  The  more  the 
work  costs,  the  more  money  the  'old  man'  makes."  The  author  knows  this 
to  be  the  case,  for  some  years  ago  he  had  to  let  a  large  contract  for  foreign 
work  at  cost  plus  a  percentage;  and  although  the  contractors  themselves 
tried  to  do  the  honest  thing  at  all  times,  their  men  "loafed"  to  such  an 
extent  that  the  final  cost  of  the  construction  was  atrociously  high;  and  he 
had  occasionally,  on  his  own  responsibility,  to  discharge  some  of  the  con- 
tractor's employees,  including  once  the  field  superintendent.  This  method 
of  letting  work  involves  asking  too  much  of  frail  human  nature. 

Method  D  involves  less  labor  in  cost-keeping  than  Method  C;  but, 
otherwise,  it  is  open  to  the  same  general  objection. 

Method  E  is  almost  as  unsatisfactory  to  the  client  as  Methods  C  and  D, 
except  that  the  contractor's  reward  for  his  own  iniquity  is  a  fixed  quantity 
and  not  in  direct  proportion  to  the  extent  of  that  iniquity. 

Method  F  involves  a  slight  improvement  on  Method  E,  but  only  to  the 
extent  of  a  little  simphfication  in  bookkeeping  and  perhaps  a  reduced 
opportunity  for  "squeezing"  the  chent. 

The  author  readily  acknowledges  that  during  war  times,  when  the  trend 
of  the  market  for  both  materials  and  labor  was  rapidly  upward,  no  con- 
tractor could  have  afforded  to  take  work  either  for  a  lump  sum  or  by  unit 
prices.  Unfortunately,  in  order  to  bring  the  war  to  a  successful  conclusion, 
a  vast  amount  of  public  work  had  to  be  done  with  the  utmost  despatch, 
irrespective  of  what  the  cost  might  be ;  hence  the  Government  had  no  choice 
at  all  in  the  matter,  and,  consequently,  it  let  many  millions  of  dollars, 
worth  of  contracts  at  "cost  plus  a  percentage"  or  "cost  plus  a  lump  sum." 
If  the  true  history  of  all  such  contracts  was  ever  written  and  made  public, 
the  nation  would  stand  aghast  at  the  extravagance  they  involved;  and 
those  two  methods  of  contract-letting  would  receive  the  universal  condem- 
nation of  all  intelligent,  disinterested  persons. 

As  was  stated  in  the  oral  discussion  of  Mr.  Clarke's  paper,  when  a 
contractor  has  simultaneously  two  or  more  contracts,  one  of  which  is  on 
the  "cost  plus"  basis  and  the  other  or  others  on  either  the  "lump-sum" 
or  the  "unit-price"  basis,  he  will  naturally  put  his  best  and  most  ener- 
getic men  on  the  latter,  and  will  shift  the  lazy  and  incompetent  ones  to 
the  former.  This  practice  has  become  so  well  established  by  custom  that 
the  "cost  plus"  contracts  have  been  dubbed  "hospital  jobs";  and  it 
appears  that  the  nickname  has  stuck. 

Is  it  not  obvious  that  anyone  who  lets  a  contract  on  the  "cost  plus" 
basis  places  himself  absolutely  at  the  mercy  of  the  contractor  and  the 
contractor's  employees?     It  is  true  that  the  specifications  often  contain 


342  ECONOMICS   OF   BEIDGEWORK  Ch.\i'ter  XXXIII 

restri'^tions  which  tend  to  lessen  the  contractor's  power  to  take  advantage 
of  the  cHent ;  but  their  enforcement  would  be  very  troublesome,  and  would 
generall}'  involve  Utigation  with  its  attendant  delay  and  expense. 

Most  people  will  acknowledge  that  the  percentage  of  truly  conscientious 
contractors  is  not  overwhelming^  large,  but  how  much  smaller  is  that  of 
truty  conscientious  workmen!  The  author  does  not  deny  that  there  are 
worlonen  who  always  give  a  quid  pro  quo  and  who  are  upright  and  honor- 
able in  all  their  dealings;  but,  alas,  they  are  sadly  in  the  minority.  Their 
number  is  so  small  that  they  are  unable  to  induce  their  co-laborers  to  exert 
themselves  any  more  than  they  are  compelled  to,  unless  they  are  paid  bj-  the 
job  instead  of  by  the  day  or  hour. 

By  the  way,  when  it  is  practicable,  such  a  scheme  of  paj'ing  the  work- 
men is  an  improvement  on  that  of  time  compensation,  because  it  provides 
a  great  incentive  to  effort;  but,  at  the  same  time,  it  also  serves  as  a  strong 
temptation  to  scamp  the  work.  "With  close  supervision,  however,  and  a 
strict  enforcement  of  the  clause  in  the  specifications  relating  to  the  taking 
out  and  replacing  of  defectively  built  work,  the  employees  soon  learn, 
through  the  fines  and  penalties  enforced  by  the  contractor,  that  scamping 
does  not  pay,  and  that  the  old  adage  of  honesty  being  the  best  policy  is 
just  as  apphcable  now  as  it  was  when  first  enunciated. 

Method  G  involves  only  a  very  shght  modification  of  that  of  ''cost 
plus  a  lump  sum,"  the  said  lump  sum  being  replaced  by  another  sum 
obtained  by  adding  together  the  products  of  the  actual  quantities  of  all  the 
materials  by  certain  small  unit  prices  agreed  on  in  the  contract.  Although 
the  author  concedes  that  this  method  is  undoubtedly  the  best  of  all  the 
straight  "cost-plus"  methods,  it  possesses  all  the  serious  objections  inherent 
thereto. 

In  addition  to  those  previously  indicated,  there  might  be  mentioned  the 
fact  that  any  straight  ''cost-plus"  basis  effectively  cuts  out  competition, 
and  advantages  a  favored  few  of  the  larger  and  more  experienced  con- 
tractors, rendering  it  difficult  for  the  smaller  and  less  experienced  ones  to 
secure  any  work,  except  through  some  other  method  of  letting.  It  ought  to 
be  evident  to  anyone  possessed  of  ordinary  vision  that  such  a  method  will 
militate  toward  cutting  the  "small  fry"  contractors  out  of  bidding;  for 
when  an  owner  is  wilhng  to  let  a  piece  of  work  on  any  straight  "cost-plus" 
basis,  he  naturally  will  want  to  award  it  to  a  large  contractor  of  means, 
who  has  an  esta,blished  reputation  for  fairness  and  efficiency.  That  would 
practically  mean  letting  all  contract  work  without  competition,  and 
American  contractors,  as  ai  body,  would  object  seriously  to  any  such 
procedure.  It  is  true  that  the  owner  might  call  for  competitive  bids  on  the 
basis  of  having  each  bidder  name  a  lump-sum  as  a  fixed  net  fee,  and  award- 
ing the  contract  to  the  competitor  who  quotes  the  lowest  figure;  but  the 
adoption  of  such  a  method  would  often  result  in  serious  trouble,  delay,  and 
expense,  and  would  not  ensure  that  the  work  would  go  to  the  most 
desirable  bidder. 


ECONOMICS   IN   CONTRACT   LETTING  343 

Under  the  heading  TI,  a  number  of  profit-sharing  methods  have  been 
tried  and  have  proved  to  be  more  or  less  satisfactory.  All  of  them  neces- 
sarily presuppose  a  careful  accounting  of  cost  from  start  to  finish.  Unless 
the  contract  between  the  two  parties  clearly  indicates  how  every  main 
detail  of  cost  is  to  be  computed,  there  will  be  trouble  before  the  work  is 
finished.  For  instance,  in  respect  to  plant — does  the  contractor  furnish 
it  free  of  charge,  or  does  he  receive  rental  for  it,  with  the  rental  charged  as 
one  of  the  items  of  cost  of  the  work?  How  about  paying  for  repairs  and 
renewals  to  plant?  Who  stands  the  expense  of  these  items — does  the  con- 
tractor, or  is  it  charged  as  an  item  of  cost  of  doing  the  work?  Again,  if 
extra  work  is  done  under  the  contract,  how  is  it  to  be  counted  when  making 
the  final  settlement? 

It  requires  the  service  of  an  expert  consulting  engineer  or  that  of  an 
experienced  contractor  to  draft  a  contract  and  specifications  which  will 
provide,  in  a  manner  satisfactory  to  both  parties,  for  all  possible  contingen- 
cies. With  such  papers,  however,  and  with  a  close  system  of  cost-account- 
ing, this  general  method  of  profit-sharing  is  the  most  satisfactory  scheme 
for  contract-letting  which  can    be  evolved. 

None  of  the  modified  methods  of  the  "cost-plus"  system,  involving 
some  means  or  other  of  profit-sharing,  which  have  yet  been  tried  in  practice, 
can  be  said  to  be  entirely  satisfactory  to  the  owner,  though  possibly  so  to 
the  contractor,  in  that  they  all  fail  to  put  a  limit  on  the  total  cost  of  the 
construction  or  to  penalize  a  contractor  who,  through  either  wilfulness  or 
carelessness,  allows  the  cost  of  construction  to  pass  the  bounds  of  reason. 
It  does  not  suffice  to  stipulate  in  the  contract  that,  when  the  total  cost  passes 
a  certain  amount,  the  allowance  for  profit  is  gradually  to  be  reduced  until  a 
certain  minimum  limit,  however  small  it  may  be,  is  reached.  The  setting  of 
that  limit  leaves  the  contractor  in  a  position  to  take  fife  easily  and  to  avoid 
personal  worry  after  his  hard  luck  has  attained  to  a  certain  magnitude; 
for,  subsequently  to  that,  he  will  lose  nothing  but  his  time  and  the  possible 
use  of  his  plant  on  some  remunerative  contract,  while  the  owner  will  have 
to  pay  whatever  additional  amount  the  job  may  cost.  On  this  point  the 
writer  knows  whereof  he  speaks;  because  one  of  the  war-time  contracts 
engineered  by  his  firm  was,  of  necessity,  let  on  that  basis,  and  the  results 
thereof  are  siriply  sickening.  The  chent  was  left  at  the  mercy  of  the  con- 
tractor, and  the  totil  cost  proved  to  be  excessive. 

From  the  preceding  it  is  evident  that  the  ''cost-plus,"  the  "lump  sum," 
and  the  "unit-price"  methods  of  letting  contracts  are  not  only  faulty,  but 
also  unjust  to  one  or  other  of  the  two  parties  to  the  agreement;  conse- 
quently, the  question  arises:  "Is  there  not  some  method  which  will  be 
just  and  fair  to  both?  That  question,  the  writer  claims,  can  truly  be 
answered  in  the  affirmative;  but  before  proceeding  to  explain  such  a  method 
in  complete  detail  there  will  be  presented  a  statement  of  the  main  require- 
ments of  an  ideal  system. 

Salient  Features  of  an  Ideal  System,  of  Contract-Letting  and  Profit-Shar- 


344  ECONOMICS   OF   BRIDGEWORK  Ch.^ter  XXXIII 

ing.     The  essential  requirements  of  an  ideal  tj'pe  of  contract  are  as  fol- 
lows: 

First.     It  must  provide  a  means  of  sharing  with  the  workmen  on  an 

equitable  basis  the  total  net  profit  on  the  job. 
Second.     It  must  set  some  kind  of  a  limit  to  the  total  cost  of  the  work, 
so  as  to  prevent  a  careless,  incompetent,  or  conscienceless  contractor 
from  running  up  the  expense  to  an  outrageously  great  amount. 
Third.     It  must  reduce  to  a  minimum  the  chance  of  the  contractor's 
being  out  of  pocket  on  the  completion  of  the  work,  unless  such  con- 
dition is  due  to  his  own  carelessness  or  lack  of  push. 
Fourth.     It  must  retain  all  the  advantages  of  competitive  bidding,  so 
as  to  give  every  capable  and  worthy  contractor  who  is  desirous  of 
figuring  on  the  work  an  even  chance  of  securing  the  contract. 
Fifth.     It  must  provide  an  incentive  for  the  contractor  and  all  his 
assistants  and  workmen  to  use  every  legitimate  effort  to  make 
the  work   as   inexpensive   as   possible,   without  violating  in  any 
manner  the  requirements  of  the  specifications. 
Sixth.     It  must  provide  a  just  and  equitable  basis  of  payment  for  a 
possible  increase  in  the  estimate  of  total  quantities  and  for  adjusting 
satisfactorily  to  all  concerned  the  reduction  of  payment  due  to  a 
possible  diminution  thereof. 
Seventh.     It  must  ensure  that  the  owner  will  be  acting  for  his  own  best 
interests  by  aiding  the  contractor  in  every  possible  way  to  com- 
plete his  work  quickly  and  inexpensively,  provided,  of  course,  that 
it  is  done  in  such  a  manner  as  to  guarantee  the  attainment  of  the 
owner's  ultimate  purpose,  as  expressed  in  the  specifications. 
Eighth.     Its  provisions  must  be  such  as  to  keep  constantly  in  good 

humor  every  one  connected  with  the  construction. 
Ninth.     Its  method  of  final  settlement  of  accounts  must  be  clear,  simple, 
?nd  easy  of  application;  and  the  keeping  of  them  during  the  prog- 
ress of  the  work  must  be  no  more  complicated  or  expensive  than  it 
would  be  in  the  case  of  any  ordinary  "  cost-plus "  contract. 
Description  of  the  Ideal  Method.     Let  the  specifications,  which  should 
invariably  be  drafted  by  an  engineer  who  is  acknowledged  to  be  an  expert 
in  the  class  of  work   covered  in  the  proposed  contract,  be   complete  and 
thorough  in  every  detail,  recording  all  that  is  known  concerning  the  govern- 
ing conditions;   pointing  out  all  featm-es  about  which  there  is  any  uncer- 
tainty; tabulating  as  accurately  as  possible  the  estimated  quantities  of  all 
the  materials  that  will  probably  enter  the  construction;  providing  a  justly- 
drawn  clause  for  unclassified  work  and  the  payment  theix^for;    calling  for 
each  bidder  to  submit  in  full  detail  his  estimate  of  actual  cost  of  doing  the 
work  by  applying  to  all  quantities  of  materials  given  in  the  s]i(H'ifi(';vtions, 
unit-(;ost  prices  (termed  Schedule  A),  each  price  containing  a  projiortionate 
share  of  any  contingency  allowance  that  may  have  been  made,  totaling  the 
products  so  as  to  form  ''Sum  A,"  and  adding  thereto  the  amount  of  profit 


ECONOMICS   IN   CONTRACT   LETTING  345 

which  he  has  decided  to  ask,  thus  making  "Sum  B."  This  last  amount 
will,  in  reality,  represent  the  bidder's  tender;  but  to  it  there  will  be  added 
a  profit  for  the  owner,  exactly  equal  to  that  asked  for  by  the  successful 
bidder,  and  another  profit  or  bonus  for  the  employees,  amounting  to  a 
previously  fixed  percentage  (say,  20  or  25)  of  the  sum  of  the  aforesaid  prof- 
its of  the  contractor  and  the  owner,  thus  making  "Sum  C."  This  last  sum 
is  the  temporary  limit  of  total  expenditure  on  the  part  of  the  owner,  pred- 
icated upon  the  assumption  that  the  approximate  quantities  of  materials 
given  in  the  specifications  are  correct;  and  it  is  on  the  basis  of  these  "Sums 
C"  that  bids  will  be  compared  and  the  award  of  the  contract  made.  The 
ratio  r  of  "Sum  C"  to  "Sum  A"  is  to  be  applied  to  each  of  the  unit  prices 
used  in  the  preparation  of  the  cost  estimate,  in  order  to  obtain  the  list  of 
unit  prices  (termed  "Schedule  B")  to  apply  temporarily  to  the  actual 
quantities  of  materials  in  the  completed  construction,  when  making  the 
final  adjustment  of  accounts. 

If  there  are  any  items  of  expense  of  construction  not  covered  by  the  list 
given  in  the  specifications,  the  clause  of  the  latter  relating  to  "Unclassified 
Work"  will  take  care  of  them.  That  clause  should  stipulate  that,  for  aU 
such  unlisted  items,  the  actual  cost  of  labor  and  materials  therefor,  without 
any  allowance  for  superintendence  or  overhead,  is  to  be  recorded ;  and  to  it 
is  to  be  added  later  30%  of  its  amount  to  allow  for  superintendence,  over- 
head, and  the  various  profits.  This  sum  is  to  be  added  to  the  total  value  of 
the  actual  quantities  of  all  the  materials  listed  in  the  specifications  figured 
at  the  proportionately  increased  unit  prices  as  given  in  "Schedule  B"; 
and  the  result,  "Sum  D"  (with  a  single  modification  explained  hereinafter), 
will  be  the  final  limiting  cost  to  the  owner  and  the  basis  for  computing  the 
net  profits  to  be  divided  between  the  contractor,  the  owner,  and  the  work- 
men. 

The  specifications,  of  course,  will  contain  a  clause  providing  a  surety 
company  bond  for  the  faithful  performance  of  the  work  and  for  guarantee- 
ing the  client  against  having  to  pay  more  than  the  limiting  sum  agreed  on 
(as  finally  modified). 

Method  of  Profit-Sharing  Contract.  The  following  method  of  profit-shar- 
ing between  the  contractor,  the  owner,  and  the  employees  is  to  be  adopted: 

An  accurate  estimate  of  cost  of  every  detail  of  the  work  from  start  to 
finish  is  to  be  kept  by  the  contractor  and  verified  by  an  accountant  in  the 
employ  of  the  cKent,  so  that  the  total  profit  on  the  job  may  be  ascertained 
by  deducting  this  total  cost  from  the  maximum  figure  named  in  the  con- 
tractor's tender  and  afterward  embodied  in  the  contract  (modified,  how- 
ever, as  hereinafter  described).  This  profit,  less  the  amount  of  the  employ- 
ees' bonus,  is  to  be  shared  between  the  contractor  and  the  client  as  indicated 
in  the  profit  diagram,  Fig.  33a*.    It  should  be  clearly  understood  that  every 

*  Mr.  Hardesty  has  pointed  out  the  fact  that  on  large  contracts  the  curves  cannot 
be  read  with  sufficient  accuracy  for  a  proper  final  settlement  of  the  account,  and  that 
much  trouble  might  be  engendered  thereby  between  the  accountants  of  the  two  parties. 


346 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XXXIII 


direct  and  indirect  expense  to  which  the  contractor  is  put  in  doing  the  work, 
after  the  contract  is  signed,  is  to  be  included  in  the  cost — all  overhead 
expenses  of  every  kind,  plant  deterioration,  travehng  expenses,  supervision, 
and  salaries,  excepting  only  that  the  contractor  hmiself  is  not  entitled  to 
any  salary.  In  the  case  of  a  firm  being  the  contractor,  the  head  of  that 
firm  should  receive  no  salary;  but  if  any  of  the  juniors  devote  their  time 
exclusively  to  the  job,  it  would  be  legitunate  to  allow  them  reasonable 
salaries,  equivalent  to  what  would  have  to  be  paid  to  regular  assistants. 
All  such  matters,  of  course,  should  be  stipulated  in  the  contract. 

In  order  to  determine,  after  the  entire  job  is  finished,  the  amount  due 
the  contractor,  "Sum  C"  is  to  be  subtracted  from  "Sum  D,"  and  the  ratio 
which  this  difference  (either  a  positive  or  a  negative  quantity)  bears  to 


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DIAGRAM    FOR   PROFIT  SHARING 

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012345678   9  10  U  12  1314  15  1617  IS  19  20  2122  23  24  25  26  27  28  29  30  3U2  33  3'H35  36  37 
Total  Percentage  of  Saving  on  Limiting  Cost  to  Client 

Fig.  33a.     Total  Percentage  of  Saving  on  Limiting  Cost  to  Client. 


"Sum  C"  is  to  be  figured  and  adopted  in  the  use  of  the  diagram  of  "cor- 
rective ratios"  (Fig.  336*)  for  the  said  difference. 

Application  of  Corrective  Ratio.  There  are  two  reasons  for  applying 
this  corrective  ratio: 

First.     In  the  case  where  the  actual  quantities  of  materials  exceed  the 


The  solution  of  the  difficulty  is  to  substitute  a  broken  line  for  each  curve,  passing 
through  the  known  points  at  zero,  five,  ten,  fifteen,  and  twenty  percentages.  The 
readings  for  these  points  on  the  upper  line  are  zero,  four,  seven,  nine,  and  ten;  and 
on  the  lower  line  they  are  zero,  one,  three,  six,  and  ten.  Such  an  arrangement  removes 
every  possibiUty  of  dispute  concerning  the  reading  of  the  diagram,  because  all  per- 
centages intermediate  to  the  above-mentioned  ones  can  be  directly  interpolated. 

*  The  curve  in  this  diagram  is  intended  to  be  the  quadrant  of  a  circle;  hence,  if  in 
reading  it  there  be  any  dispute  between  the  accountants  of  the  two  parties,  it  can  be 
settled  by  drawing  the  cvn-ve  on  cross-section  paj^er  using  a  large  scale,  or  by  employing 
exact  mathematical  formulae. 


ECONOMICS   IN   CONTRACT  LETTING 


347 


estimated  ones  of  the  specifications,  it  would  be  hardly  fair  to  the  owner 
to  apply  to  the  excess  those  unit  prices  which  produce  his  tentative  Hmiting 
expenditure. 

Second.  In  the  case  where  the  actual  quantities  of  materials  are  less 
than  the  estimated  ones,  it  would  be  unjust  to  the  contractor  to  use  the 
high  unit  prices  on  the  diminution  quantities,  not  only  because  of  the  great 
difference  between  these  and  the  unit  actual  costs,  but,  also,  for  the  reason 
that  the  total  overhead  charges  would  be  about  the  same  for  the  dimin- 
ished amounts  as  for  the  estimated  total  quantities. 


1.00 
0.99 


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DIAGRAM    OF    CORRECTIVE   RATIOS 

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,00..01 .02  .02  .04 .05  .06  .07  .08  .09  .10  .11  .12  .13  .14  .15  .16  .17  .18  .19  .20  .21 .22  .23  .24  .25 
Ratios  of  Value  Difference 

Fig.  336.     Diagram  of  Corrective  Ratios. 


In  the  corrective  ratio  diagram  (Fig.  336)  it  will  be  noticed,  that,  after 
the  ratio  of  value  difference  (due  to  increase  or  diminution  of  quantities 
of  materials)  reaches  0.2,  the  "corrective  ratio"  remains  constant  at  0.8, 
which  corresponds  approximately  to  actual  cost  conditions.  The  object 
of  this  is  to  provide  that  the  contractor  shall  not  be  too  much  benefited 
by  an  abnormal  increase  in  quantities,  nor,  on  the  other  hand,  shall  he 
be  at  too  much  disadvantage  because  of  an  abnormal  diminution  thereof. 

To  utiHze  the  corrective  ratio  diagram  (Fig.  336)  look  on  the  line  of 
abscissae  for  the  ratio  of  cost  difference,  pass  vertically  upward  to  the 
curve  (or  right  line,  as  the- case  may  be),  then  horizontally  to  the  extreme 


348  ECONOMICS   OF  BRIDGEWORK  Ch.a.pter  XXXIII 

left  vertical,  which  will  indicate  the  corrective  ratio  reqmred.  Next,  mul- 
tiply the  previously  computed  difference  by  this  corrective  ratio,  and  add 
the  result  to  or  subtract  it  from  "Sum  C."  The  result,  ''Sum  E,"  will 
be  the  finally  corrected  limit,  from  which  must  be  subtracted  the  total 
actual  cost  so  as  to  determine  the  amount  of  profit  to  be  divided.  The 
first  step  in  such  division  is  to  set  aside  the  employees'  share  on  the  basis 
of  percentage  agreed  on;  and  the  next  is  to  divide  the  remaining  profit 
between  the  contractor  and  the  owner,  as  per  the  profit  diagram  (Fig.  33a). 
The  size  of  the  percentage  of  the  declared  profit  to  allow  the  employees 
will  depend  on  the  character  of  the  work  covered  in  the  contract  in  respect 
to  the  proportionate  division  of  the  cost  between  materials  and  labor. 
Under  ordinary  conditions,  the  division  is  about  half  and  half,  in  which 
case  the  employees'  percentage  should  be  from  20  to  25;  but  where  the 
labor  cost  preponderates  these  figures  should  be  increased,  and  where  the 
materials  cost  is  the  greater  they  should  be  diminished. 

In  respect  to  the  division  of  this  bonus  among  the  employees,  the  fol- 
lowing method  is  suggested : 

Only  those  workmen  or  assistants  of  any  class  who  have  stayed  on  the 
job,  either  until  its  completion  or  until  their  services  were  no  longer  needed, 
should  participate  in  the  profits;  and  the  amount  of  the  share  of  each  such 
workman  and  assistant  should  be  in  the  proportion  which  his  total  earning 
on  the  work  bears  to  the  grand  total  of  the  earnings  of  all  those  employees 
who  so  participate.  As,  in  any  good  business  organization,  a  record  is 
always  kept  of  the  amount  of  salary  or  wages  paid  to  each  employee  on 
any  contract,  it  would  require  only  a  few  hours  of  extra  work  for  the  book- 
keeper, after  the  job  is  finished,  to  compute  each  man's  proportionate 
share  of  the  bonus. 

There  is  an  additional  protection  against  possible  loss  which  might  be 
given  to  the  contractor  under  certain  conditions,  especially  on  work  to  be 
done  in  a  foreign  country.  If  it  be  anticipated  that  during  construction 
any  large  general  rise  in  the  price  of  labor  is  likely  to  occur,  thus  greatly 
augmenting  the  total  cost  of  the  work,  the  hmiting  total  expenditure  of 
the  owner,  as  hereinbefore  finally  adjusted,  should  be  increased  by  an 
amount  figured  thus: 

Determine  the  average  current  wages  for  common  labor  at  the  time  of 
letting  the  contract,  and  the  average  paid  therefor  during  the  entire  tune 
occupied  by  the  construction,  and  call  the  ratio  of  these  two  averages  r'; 
then  figure  the  total  amount  of  salaries  and  wages  paid  to  employees  from 
start  to  finish  and  call  it  W.    Then, 

Tf(/-l)Xl.2 

will  be  the  amount  required,  the  factor,  1.2,  covering  a  fair  allowance  for 
overhead  and  profits. 

It  has  been  suggested  of  late  in  the  technical  press  that  the  contractor 
himself  should  be  paid  a  salary  by  the  owner,  in  addition  to  whatever 


ECONOMICS   IN   CONTRACT   LETTING  S49 

profit  he  may  make  on  the  job.  Such  a  pohcy  would  be  simply  suicidal 
on  the  part  of  the  owner,  for  if  the  work  were  to  be  handled  badly,  the 
contractor  might  continue  to  earn  money  while  the  owner  would  be  losing 
heavily.  The  writer  has  met  with  just  such  a  case;  hence,  in  this  particu- 
lar, he  certainly  knows  whereof  he  speaks.  Such  a  practice  should  never, 
under  any  conditions,  be  countenanced  by  either  the  owner  or  his  engineer. 

Exemplification.  In  order  to  illustrate  the  modus  operandi  of  this 
method  of  profit-sharing,  let  us  assmiie  the  following  case,  in  which  the 
estimated  quantities  are  exceeded.  For  the  purpose  of  simplification  in 
figuring,  round  numbers  have  been  assumed  for  both  the  quantities  of 
materials  and  the  unit  costs  thereof.  The  job  is  one  of  railroad  construction 
and  the  number  of  items  is  intentionally  limited  for  the  sake  of  convenience. 

The  following  are  the  quantities  of  materials  supposed  to  be  stated  in 
the  specifications: 

Earthwork,  measured  in  cutting 1,000,000  cu.  yds. 

Loose  rock,           "         "       "      .........  100,000       " 

SoHdrock,            "         "       " 40,000      " 

Concrete  in  structures. . 10,000       " 

Wooden  trestle. 2,000  Hn.  ft. 

Structural  steelwork,  erected. ...........  500,000  lbs. 

The  tender  of  the  successful  bidder  was  as  follows : 

Quantities.             Schedule  A.  Totals. 

Earthwork 1,000,000  cu.  yds.  @  $0 .  50  =  $500,000 

Loose  rock 100,000       ''        @  1.00  =  100,000 

Solid  rock 40,000       "        @  1.50=  60,000 

Concrete. 10,000       "        @  20 .  00  =  200,000 

Wooden  trestle 2,000  Un.  ft.    @  50.00  =  100,000 

Steelwork..... 500,000  lbs.         @  0.08  =  40,000 


Total  estimated  cost  ("Sum  A")  •  =  •  •  • =  $1,000,000 

Profit  required,  10%. =         100,000 


Tender  C'Sum  B") =  $1,100,000 

Allowance  for  owner's  profit —        100,000 

Employees'  profit,  25%  of  $200,000. =  50,000 


Temporary  limit  ("Sum.  C"). =  $1,250,000 

SumC    $1,250,000 
Katio,  r-Q^^  ^  ~  $1,000,000     ^'"^^^ 

The  proportionately  increased  unit  prices,  therefore,  will  be  as  follows: 


350  ECONOMICS  OF  BRIDGEWORK  Chapter  XXXIII 

Schedule  B. 

Earthwork $0.50X1.25  =  $0.625 

Loose  rock 1.00X1.25=   1.25 

Solid  rock 1.50X1.25=    1.875 

Concrete 20.00X1.25  =  25.00 

Wooden  trestle 50.00X1.25  =  62.50 

Steelwork 0.08X1.25=  0.10 

The  actual  quantities  of  the  materials  in  the  completed  job  were,  as 
follows : 

Earthwork 980,000  cu.  yds. 

Loose  rock 110,000      " 

Solid  rock 50,000      " 

Concrete 10,500      " 

Wooden  trestle 2,100  lin.  ft. 

Steelwork 480,000  lbs. 

In  addition,  there  was  done  by  the  contractor  certain  "unclassified 
work  "  which  actually  cost  him  for  labor  and  materials  $20,000. 
The  revised  estimate  is,  therefore,  as  follows: 

Earthwork 980,000  cu.  yds.  @  SO .  625  =  $612,500 

Loose  rock 110,000      "        @  1.25   =  137,500 

SoHdrock 50,000      "        @  1.875=  93,750 

Concrete 10,500      "        @  25 .00   =  262,500 

Wooden  trestle 2,100  lin.  ft.    @  62.50=  131,250 

Steelwork 480,000  lbs.         @  0 .  10  =  48,000 

Unclassified  work $20,000X  1 . 3  =  26,000 


Summation,  or  "Sum  D" =$1,311,500 

The  difference  between  "Sum  D"  and  "Sum  C"  equals 

$1,311,500-$1,250,000  =  $61,500. 

$61,500 
Ratio  of  difference  =  ^ ..  ^ ^„  ^^^  =  0 .  0492 ;  say,  0.05. 

For  this  ratio,  the  diagram.  Fig.  33fo,  gives  a  corrective  ratio  of  0.865, 
which  multiplied  by  $61,500  gives  $53,198,  say,  $53,200,  making  the  cor- 
rected limit,  or  "Sum  E,"  =  $l,250,000+$53,200  =  $1,303,200. 

If  the  total  actual  cost  of  the  work,  including  that  of  the  imclassified 
work  without  allowance  for  superintendence  or  overhead,  amounted  to 
$1,100,000,  the  total  profit  would  be: 

$1,303,200- $1,100,000  =  $203,200. 

Of  this,  the  joint  share  of  the  contractor  and  the  owner  would  be: 

$203,200-^1. 25  =  $162,560; 


ECONOMICS   IN   CONTRACT   LETTING  351 

and  the  employees'  bonus  would  be: 

$203,200  -  $162,560  =  $40,640. 

which  is  exactly  25%  of  $162,560. 

In  respect  to  the  division  of  this  last  amount  between  the  contractor 
and  the  owner,  its  ratio  to  total  cost  is: 

$162,560^ $1,100,000  =  0.148,  or  14.8%. 

From  the  diagram  for  profit  division  (Fig.  33a)  we  find  the  division  of  this 
percentage  to  be: 

Contractor 8.9% 

Owner 5.9% 

This  makes  the  total  payment  by  the  owner  to  the  contractor: 

$1,100,000X  108 . 9  =  $1,197,900. 

Let  us  now  take  a  case  where  there  is  a  diminution  in  the  estimated 
quantities  of  materials.  Using  the  same  case  as  before  in  respect  to 
estimated  quantities  and  tender,  we  shall  assume  the  following  actual 
quantities  of  materials: 

Earthwork 1,050,000  cu.  yds. 

Loose  rock 50,000      " 

Solid  rock 20,000     '' 

Concrete 8,000      '' 

Wooden  trestle 1,800  Hn.  ft. 

Steel  work 450,000  lb. 

The  cost  of  the  unclassified  work  was  $20,000,  as  in  the  preceding  case. 
The  revised  estimate  is,  therefore,  as  follows: 

Earthwork 1,050,000  cu.  yds.  @  $0 .  625  =  $656,250 

Loose  rock 50,000      ''        @  1.25  =  62,500 

Solid  rock 20,000      "        @  1.875=  37,500 

Concrete 8,000      ''        @  25.00=  200,000 

Wooden  trestle 1,800  lin.  ft.    @  62.50  =  112,500 

Steelwork 450,000  lb.          @  0 .  10  =  45,000 

Unclassified  work $20,000X1 .3=  26,000     , 


Summation,  or  "Sum  D" =  $1,139,750 

The  difference  between  "Sum  D"  and  "Sum  C"  equals 

$1,139,750-$1,250,000= -$110,250. 

$110,250 
Ratio  of  difference  =  ^rr?7?7r7^7^  =  0-0882. 
!t)l,^oU,000 


352  ECONOMICS   OF   BRIDGEWORK  Chapter  XXXIII 

For  this  ratio,  the  diagram  gives  a  corrective  ratio  of  0.835,  which, 
multipUed  by  $110,250,  gives  $92,059,  say,  $92,100,  making  the  corrected 
limit. 

''  Sum  E  "  =  $1,250,000-  $92,100  =  $1,157,900. 

If  the  total  actual  cost  of  the  construction,  including  that  of  the  unclassi- 
fied work  without  allowance  for  superintendence  or  overhead,  amounted  to 
$880,000,  the  total  profit  would  be: 

$1,157,900  -  $880,000  =  $277,900. 

Of  this,  the  joint  share  of  the  contractor  and  the  owner  would  be: 

$277,900  -^  1 .25  =  $222,320, 

and  the  employees'  bonus  would  be: 

$277,900  -  $222,320  =  $55,580, 

which  is  exactly  25%  of  $222,320. 

In  respect  to  the  division  of  this  last  amount  between  the  contractor 
and  the  owner,  its  ratio  to  total  cost  is: 

$222,320 -^ $880,000  =  0.253,  or  25.3%. 

From  the  diagram  for  profit  division,  (Fig.  33a) ,  we  find  the  division  of 
this  percentage  to  be  on  the  "fifty-fifty"  basis,  making  the  total  payment 
by  the  owner  to  the  contractor  =  $880,000  X  1.1265  =  $991,320. 

Advantages.  The  advantages  of  this  method  of  contract-letting  are  as 
f  pUows : 

First.  While  it  is  true  that  the  client  at  the  outset  does  not  know 
exactly  what  the  work  is  going  to  cost  him,  he  is  positive  that  it  will  not 
cost  him  materially  more  than  a  certain  amount,  provided  his  engineer's 
estimate  of  quantities  is  about  right,  as,  generally  speaking,  it  certainly 
ought  to  be. 

Second.  The  client  has  the  satisfaction  of  feeling  that  even  if,  in  his 
opinion,  the  limit  determined  by  the  contractor's  bid  is  excessive,  and  that 
the  final  net  profit  on  the  job,  in  consequence,  will  be  too  large,  the  said 
net  profit  will  be  shared  between  them  on  a  ''fifty-fifty"  basis. 

Third.  While  the  client  is  bound  to  pay  a  certain  percentage  of  the 
joint  profit  as  a  bonus  to  the  contractor's  employees,  generally  he  will  not  be 
out  of  pocket  thereby,  but,  on  the  contrary,  he  will  gain;  because  the  incen- 
tive that  the  prospective  bonus  gives  to  all  hands  to  labor  energetically  will 
save  in  the  total  cost  much  more  than  the  amount  of  the  bonus. 

Fourth.  All  the  advantages  of  competitive  bidding  are  retained  by  this 
method,  because  the  fully-capable  competitor  who  tenders  the  lowest 
amount  for  "Sum  C"  should  be  awarded  the  contract.  All  bids  will  be  on 
exactly  the  same  basis,  no  modification  of  the  stipulated  method  of  tender- 
ing being  permitted.     It  is  understood,  of  course,  that  the  contract  will  not 


ECONOMICS   IN   CONTRACT   LETTING  353 

be  awarded  to  any  competitor  who  docs  not  possess  the  necessary  experi- 
ence, capital,  and  plant,  and  who  has  not  an  established  reputation  for 
doing  good  and  satisfactory  work. 

Fifth.  The  contractor,  if  he  was  not  too  keen  in  bidding,  knows  that 
there  is  almost  no  chance  whatsoever  of  his  losing  money  on  the  job; 
because  before  doing  so  he  would  have  to  use  up  his  allowance  for  contin- 
gencies, his  own  estimated  profit,  a  profit  of  like  amount  allowed  for  the 
owner,  and  a  substantial  sum  representing  the  employees'  bonus.  If  he 
ever  does  use  up  all  these  safeguards,  the  chances  are  many  to  one  that  the 
fault  therefor  is  entirely  his  own,  being  due  to  his  negligence,  lack  of  fore- 
thought, or  deficiency  in  energy  and  push;  and  in  that  event  he  certainly 
would  deserve  to  be  penahzed. 

Sixth.  All  the  workmen  and  salaried  employees  of  the  contractor  will 
be  satisfied  with  their  job  because  of  the  excellent  opportunity  offered  for 
extra  compensation;  and  they  will,  of  their  own  accord,  work  diligently, 
and  occasionally  even  overtime,  in  order  to  expedite  the  construction.  Of 
their  own  accord,  too,  they  will  run  off  the  job  any  employee  who  is  a 
chronic  shirker,  and  they  will  make  it  their  business  to  keep  everybody 
busy;  because  the  more  cheaply  the  construction  is  done  the  greater  will 
be  the  bonus  to  divide  among  the  faithful  employees  who  stick  by  the  work 
to  the  finish. 

Seventh.  The  method  of  profit-sharing  given  by  the  diagram  for  profit 
division  (Fig.  33a)  is  eminently  equitable,  in  that  when  the  net  amount  is 
small,  nearly  all  of  it  goes  to  the  contractor,  and,  as  it  augments,  a  con- 
tinually increasing  proportion  of  it  goes  to  the  owner,  up  to  the  point  where 
the  total  joint  profit  amounts  to  20%,  after  which  the  partition  is  on  a 
"fifty-fifty"  basis. 

It  will  be  seen  that  for  a  total  net  joint  profit  of  less  than  20%,  the  fol- 
lowing divisions  will  prevail : 

With    5%  net,  4%  goes  to  the  contractor  and  1%  to  the  owner 
With  10%  net,  7%      ""      "        "  "3%     "  ''     " 

With  15%  net,  9%      ""       "         ''  "  Q%     ""     '' 

The  20%  point  was  selected  for  equal  division  as  being  the  one  above  which 
a  contract  is  generally  deemed  by  contractors  to  be  good,  slightly  below 
which  it  is  only  fair,  and  much  below  which  it  is  bad ;  for  it  corresponds  to 
a  net  profit  of  10  per  cent.  That  is  as  small  a  margin  as  is  generally  deemed 
safe  for  any  bidder  to  tender  upon,  and  yet  it  constitutes  a  satisfactory 
profit  on  a  finished  job.  As  for  limiting  the  client's  share  of  the  profit  to 
one-half — that  is  reasonable  and  just,  because  he  would  have  no  moral 
right  to  receive  more  than  his  partner,  the  contractor.  If  the  client's  share 
were  allowed  to  increase  indefinitely,  it  is  conceivable  that,  with  a  very 
large  prospective  total  profit,  the  contractor  could  save  money  for  himself 
by  making  the  work  more  expensive. 

Any  bidder  who  tenders  on  the  basis  of  a  profit  less  than  10%  should 


354  ECONOMICS   OF   BRIDGEWORK  Chapter  XXXIII 

be  looked  on  askance  by  the  owner  and  his  engineer;  and  such  a  competitor 
should  not  be  awarded  the  contract,  unless  he  possesses  an  exceptionally 
fine  reputation  for  doing  good  work  and  for  not  quitting  liis  job  before 
finishing  it.  It  is  true  that  during  very  hard  times  many  worthy  contract- 
ors are  willing  to  work  almost  for  actual  cost,  in  order  to  keep  their  work- 
men employed;  and  in  such  cases  the  good  intention  should  be  recognized 
in  making  the  award.  Nevertheless,  it  nearly  always  proves  to  be  unsatis- 
factory to  both  the  owner  and  his  engineer  to  let  a  contract  for  anj^  piece  of 
construction  at  a  figure  below  its  real  value. 

Eighth.  The  contractor  will  feel  during  the  progress  of  the  construc- 
tion that  the  chent  is  a  partner  on  the  job,  and  that,  therefore,  he  and  his 
engineers  will  not  be  likely  to  be  unnecessarily  severe  in  their  requirements, 
also  that  they  will  permit  the  adoption  of  all  legitimate  expense-saving 
expedients,  and  will  not  demand  too  many  frills  on  the  finishing. 

Ninth.  Owing  to  the  justice  and  equity  involved  by  this  method 
of  contract-letting  and  profit-sharing,  all  concerned  in  the  execution  of 
the  work  will  labor  whole-heartedly  and  good-naturedly,  avoiding  petty 
squabbles  and  disagreements;  and  the  result  will  be  earnest,  honest  effort, 
a  satisfactory  piece  of  construction,  and  the  general  contentment  of  both 
parties  to  the  agreement. 

Tenth.  While  this  method  may  at  first  glance  have  the  appearance  of 
being  complicated,  it  is  quite  simple;  and  because  of  the  clear  manner  in 
which  it  is  explained  herein,  it  is  easily  utilized  in  any  actual  case  by  follow- 
ing one  step  at  a  time  the  directions  given.  The  nomenclature  of  "sums" 
and  "schedules"  renders  the  appUcation  of  the  method  very  easy.  More- 
over, it  must  be  remembered  that  it  is  to  be  used  only  once  for  each  con- 
tract, and  then  only  after  all  the  work  is  completed  and  the  accounts  are  in 
proper  form.  Again,  the  keeping  of  the  accounts  is  in  no  way  any  more 
compHcated  than  it  would  be  in  case  any  of  the  "cost-plus"  methods  were 
used. 

Objections  That  Have  Been  Raised  to  This  Method.  A  few  objections, 
both  orally  and  in  print,  have  been  raised  to  this  proposed  method  of 
contract-letting  and  profit-sharing;  but  they  could  not  have  been  well 
considered,  for  they  are  not  valid.  It  will  be  well  before  closing  this  dis- 
cussion to  mention  them  and  show  wherein  they  are  untenable.  They  are 
as  follows: 

A.  It  has  been  asserted  that  there  would  be  special  difficulty  in 
keeping  the  accounts;  but  there  would  be  required  therefor  exactly 
the  same  woi-k  which  would  be  necessitated  by  any  of  the  "cost-plus" 
methods.  They  all  involve  a  correct  record  of  the  amount  of  every 
legitimate  item  of  expense  to  which  the  contractor  is  put;  and  the  book- 
keeping in  any  case  would  certainly  re(|uirc  an  account  with  each  employee, 
so  as  to  show  how  much  money  had  been  paid  him  from  start  to  finish. 

B.  It  has  been  claimed  that  the  method  is  too  complicated  to  be  use- 
ful.    On  the  contrary,  as  explained  previously,  it  is  simple;  and  the  pecul- 


ECONOMICS    IN   CONTKACT   LETTING  355 

iar  manner  of  its  presentation  herein  is  such  as  to  render  its  use  merely  a 
matter  of  following  step  by  step  certain  clearly  written  instructions.  More- 
over, as  before  indicated,  this  method  of  settlement  of  accounts  is  used  only 
once,  viz.,  after  the  completion  of  the  job. 

C.  It  has  been  stated  that  uneducated  contractors  would  have  diffi- 
culty in  understanding  the  method ;  but  the  man  who  made  this  claim  did 
the  average  American  contractor  a  grave  injustice.  The  construction 
contractors  in  this  country  are  as  bright  a  body  of  men  as  one  can  find  any- 
where; and  certainly  they  may  be  trusted  to  understand  anything  in  reason 
that  affects  their  interests. 

D.  It  has  been  claimed  that  most  contractors  have  a  general  inherent 
objection  to  sharing  profits  with  the  owner;  but  a  little  consideration  wiU 
show  that  there  is  no  sharing  of  the  requested  profit  until  after  the  estimated 
cost  of  the  work  (under  the  assumption  of  unchanged  quantities  of  mate- 
rials) has  been  exceeded.  It  was  to  clarify  this  situation  that  the  writer 
changed  his  original  idea  of  having  each  bidder  name  a  lump-sum  (corre- 
sponding to  "Sum  C")  as  a  provisional  limit  of  the  owner's  total  expendi- 
ture, and  a  fist  of  unit  prices  (corresponding  to  "Schedule  B")  which,  when 
appHed  to  the  estimated  quantities  of  the  specifications,  would  make  the 
sum  of  the  products  exactly  equal  to  the  said  lump-sum,  and  substituted 
therefor  the  method  herein  described,  viz.,  that  of  having  each  bidder  sub- 
mit in  detail  his  estimate  of  cost  and  his  desired  profit,  and  arranging  the 
method  of  determining  the  Hmiting  cost  to  the  owner  by  two  additions  to 
the  bidder's  tender.  This  change  is  simply  a  concession  to  prejudice,  and 
does  not  modify  the  method  proposed  by  the  writer  in  his  letter  pubhshed 
in  Contracting  in  its  issue  of  September  15th,  1919.  The  only  fundamental 
change  between  that  presentation  of  the  matter  and  this  one  is  the  inclusion 
herein  of  a  bonus  for  the  employees. 

E.  It  has  been  claimed  that  this  method  would  tend  to  deceive  the 
owner.  He  would  certainly  be  stupid  if  he  could  not  see  clearly  how  its 
tendency  is  to  cut  down  the  amount  that  he  will  pay  for  the  entire  work, 
and  that  it  will  set  a  just  limit  beyond  which,  under  the  worst  possible 
conditions,  he  cannot  be  compelled  to  pay  any  more. 

F.  It  has  been  stated,  as  a  reason  for  favoring  the  "cost-plus"  system, 
that  bonding  companies  favor  it  and  oppose  all  other  methods  of  contract- 
letting.  Naturally,  they  would  do  so;  because,  with  the  "cost-plus" 
method,  their  obligation  reduces  almost  to  zero,  the  risk  being  placed  solely 
on  the  owner.  In  truth,  with  that  method  adopted,  there  does  not  appear 
to  be  any  valid  reason  for  having  a  bond  at  all.  When  the  contractor  runs 
no  risk  of  loss  whatsoever,  why  a  surety  company  bond?  Possibly,  if  the 
surety  companies  would  consider  it  from  this  point  of  view,  they  would 
not  oppose  the  writer's  suggested  method  of  contract-letting;  for,  while  it 
reduces  very  greatly  the  possibility  of  loss  to  the  surety  company,  it 
does  not  destroy  that  organization's  function  by  removing  entirely  its 
raison  d'etre. 


356  ECONOMICS   OF   BRIDGEWORK  Chapter  XXXIII 

G.  The  claim  has  been  made  that  this  method  is  not  apphcable  to 
cases  where  no  estimate  of  quantities  has  been  made  or  for  which  no 
specifications  have  been  prepared,  and  when  it  is  necessary  to  let  the  work 
without  delay.  The  correctness  of  this  claim  is  granted,  but  its  apphca- 
bihty  should  be  confined  to  war  work,  in  which  the  element  of  time  is  the 
principal  consideration.  In  civil  life,  if  a  projector  of  an  enterprise  is  in 
such  haste  to  start  his  work  that  he  has  to  omit  the  preparation  of  specifi- 
cations and  estimates  of  quantities  before  letting  the  contract,  he  certainly 
deserves  what  is  coming  to  him  in  case  it  proves  that  he  has  placed  himself 
in  the  hands  of  an  unscrupulous  contractor  on  the  "cost-plus"  basis. 

H.  It  has  been  pointed  out  that  the  law  will  prevent  certain  public 
bodies  from  letting  contracts  on  a  "cost-plus"  basis,  and  that  such  a 
ruling  might  apply  to  the  writer's  proposed  method  also.  If  such  really 
is  the  case,  the  remedy  would  evidently  be  to  modify  the  law  so  as  to 
permit  of  its  adoption;  but  would  not  the  fact  of  its  containing  a  clause 
which  sets  a  limit  to  the  contractor's  total  compensation  always  render 
the  method  legal?     This,  however,  is  a  question  for  the  lawyers  to  settle. 

I.  A  prominent  writer  on  economics  has  lately  issued  a  tirade  against 
gambling,  especially  as  it  applies  to  contractors  guaranteeing  owners 
against  the  cost  of  work  exceeding  the  amount  of  the  tender.  The  writer 
concurs  in  this  theory  to  the  extent  that  there  should  be  no  gambling  on 
the  amounts  of  assumed  quantities  of  materials,  or,  in  certain  cases,  on 
there  not  being  any  great  rise  in  the  average  price  of  labor,  or  on  possible 
loss  through  any  reasonably  great  amount  of  hard  luck;  but  there  is  cer- 
tainly nothing  unmoral  or  oppressive  in  insisting  on  his  gambling  to  the 
extent  of  guaranteeing  against  his  own  incompetency,  carelessness,  or  lack 
of  forethought.  The  writer  is  of  the  opinion  that  a  margin  against  actual 
money  loss  to  the  contractor,  consisting  of  his  estimated  amount  for  con- 
tingencies, plus  his  requested  profit,  plus  an  equal  profit  for  the  owner, 
plus  a  substantial  bonus  for  the  employees,  is  amply  large  to  guarantee  liim 
against  all  loss  through  ordinarily  unfavorable  eventualities;  and  that, 
in  ninety-nine  cases  out  of  a  hundred,  if  such  a  margin  were  exceeded,  it 
would  be  because  of  the  contractor's  own  fault. 

Adoption  of  Method.  If  this  proposed  method  of  contract-letting  antl 
profit  sharing  is  received  with  favor  by  engineers,  architects,  contractors, 
and  builders  in  general,  it  could  easily  be  adopted  as  a  standard  for  the 
country  by  calling  a  small  convention  with  a  single  representative  from  each 
of  the  leading  technical  and  railroad  societies,  contracting  oiganizations, 
bankers'  associations,  and  labor  guilds,  to  discuss  the  advisability  of  adopt- 
ing it  (or  else  some  modification  of  it)  and  to  report  the  decision  of  the 
meeting  to  the  said  })0(lies  for  their  approval.  If  any  large  group  of  clients, 
such  as  the  railroad  companies,  were  to  adopt  the  method  as  standard  and 
use  it,  very  soon  everybody  having  construction  contracts  to  let  would 
follow  their  (;xample,  thus  making  it  the  universal  standard  of  contract- 
letting  for  the  countiy — nor  would  it  be  long  before  other  American  coun- 


ECONOMICS    IN    CONTRACT   LETTING  357 

tries  would  follow  our  lead,  thus  greatly  simplifying  our  business  relations 
with  the  various  American  Commonwealths. 

Addendum.  In  all  lines  of  manufacture  the  employees  should  share  in 
the  net  annual  profits  of  the  company;  but,  in  figuring  the  yearly  cost  of 
running  the  establishment  and  doing  the  work,  there  should  be  included 
fair  salaries  for  all  the  working  officers,  6%  on  the  actual  amount  of  cash 
invested  in  the  plant  and  business  (but  not  on  the  total  capital  stock),  an 
annual  allowance  for  a  sinking  fund  to  redeem  the  bonds  or  other  indebted- 
ness of  the  organization,  and  taxes  of  every  kind.  The  net  profit  estimated 
in  this  way  should  generally  be  divided  on  the  basis  of  one-third  to  the 
employees  and  two-thirds  to  the  company,  but  sometimes,  perhaps,  on  that 
of  one-fourth  and  three-fourths.  The  reason  why  it  should  not  be  split  on  a 
"fifty-fifty"  basis  is  that  the  company  has  to  run  the  risk  of  standing  a  loss 
in  bad  years,  while  the  employees  do  not.  Only  those  employees  who  are 
still  connected  with  the  company  at  the  end  of  the  year,  or  who  have  been 
discharged  in  good  standing,  should  share  in  the  bonus;  and  their  propor- 
tionate amounts  should  be  computed  as  previously  indicated  for  the  case 
of  construction  contracts. 


CHAPTER  XXXIV 

ECONOMICS    OF    BRIDGE-ENGINEERING    OFFICEWORK 

Concerning  economics  in  the  management  of  a  bridge  engineer's 
office,  it  will  suffice  to  offer  a  few  general  principles  and  refer  the  reader  to 
Chapter  LVIII  of  "Bridge  Engineering."  It  has  been  claimed  by  some 
engineers  that  the  scheme  of  management  therein  expounded  is  far  too 
elaborate  and  costly,  some  going  so  far  as  to  state  that,  if  it  were  followed 
out  exactly,  the  expense  involved  would  eat  up  all  the  profits.  Such, 
though,  is  not  the  case,  for  while  it  is  true  that  it  is  too  expensive  for  an 
office  with  a  small  force,  it  is  not  so  for  one  handhng  simultaneously  many 
millions  of  dollars'  worth  of  bridgework,  as  did  the  author's  in  ante-bellum 
days.  It  represents  an  ideal  system  worked  out  with  great  care  and  in 
complete  detail;  and  if  it  were  utihzed  with  proper  discretion  by  bridge 
engineers,  bearing  in  mind  that  one  should  "cut  his  coat  according  to  his 
cloth,"  much  benefit  would  result. 

In  any  case,  though,  the  following  principles  should  be  observed: 

First.  All  employees  should  arrive  promptly  in  the  morning,  preferably 
a  few  minutes  ahead  of  time,  should  get  to  work  immediately,  should  work 
diUgently,  and  should  put  in  full  time.  If,  for  any  unavoidable  reason,  an 
employee  loses  some  time  from  his  work,  it  should  be  a  point  of  honor  with 
him  to  make  it  up  by  working  overtime. 

Second.  Talking  among  the  employees  during  office  hours  should  be 
reduced  to  an  absolute  minimum  consistent  with  a  proper  exchange  of 
ideas  as  to  the  development  of  the  work  of  designing  and  detailing.  No 
general  conversation  in  the  office  should  be  allowed  under  any  circum- 
stances whatsoever. 

Third.  No  visitors  should  be  permitted  to  enter  the  drafting  or  com- 
puting rooms,  and  callers  upon  employees  should  be  made  to  understand 
that  they  are  not  welcome  and  that  visiting  is  against  the  rules. 

Fourth.  No  smoking  should  be  allowed  during  office  hours.  It  takes 
valuable  time  from  the  work;  and  hot  cigarette  ashes  are  very  destructive 
to  tracings. 

Fifth.  Each  employee  should  be  made  to  attend  strictly  to  his  own 
business,  and  no  one  should  be  allowed  to  pry  into  matters  in  relation  to 
which  he  has  no  legitimate  concern. 

Sixth.  Before  any  computations  on  a  design  are  made,  full  data  should 
be  collected  therefor;  and  a  complete  list  of  the  conditions  precedent  should 
be  sent  to  the  client  for  approval  in  writing  before  any  serious  work  is  done. 

358 


ECONOMICS   OF   BRIDGE-ENGINEERING   OFFICEWORK  859 

Then,  if  later  any  changes  are  called  for  by  the  client,  they  would  be  made 
at  his  expense,  and  he  could  raise  no  vaUd  objection  to  standing  the  cost 
thereof. 

In  order  to  systematize  the  collection  of  data,  each  office  should  have  a 
printed  Hst  of  questions  or  memoranda  to  send  to  cUents,  agents,  or  field 
men;  and  these  should  be  filled  in  as  fully  as  practicable  for  each  job.  Such 
a  list  is  given  in  Chapter  XLVI  of  "Bridge  Engineering,"  but  lately  the 
author,  for  the  benefit  of  his  future  practice  (especially  in  foreign  countries) 
has  materially  elaborated  this.  He  feels  that  it  cannot  well  be  made  too 
full  or  complete,  because  the  more  one  knows  in  advance  about  the  govern- 
ing conditions  the  better  will  he  make  his  design. 

Seventh.  There  should  be  estabhshed  certain  Kmits  to  the  accuracy  of 
all  calculations,  and  these  should  be  adhered  to.  The  list  of  limits  adopted 
in  the  author's  practice  is  given  on  page  1377  of  "Bridge  Engineering." 

Eighth.  After  each  page  of  calculations  is  finished,  it  should  be  checked 
by  the  same  computer  so  that,  if  he  has  made  any  error  thereon,  it  may  be 
corrected;  and  thus  its  effect  will  not  be  carried  into  any  succeeding  pages. 

Ninth.  All  results  should  be  roughly  checked  by  the  computer,  using 
old  records  or  diagrams,  so  as  to  ensure  that  no  egregious  blunder  has  been 
made. 

Tenth.  All  calculations  should  be  checked  by  an  independent  com- 
puter before  being  turned  over  to  the  drafting  room. 

Eleventh.  Every  record,  book,  pamphlet,  and  similar  office  possession 
should  be  filed  and  indexed  so  that  it  can  be  found  at  any  time  without 
delay. 

Twelfth.  Enough  drawings  should  be  made  to  enable  the  contractor  to 
prepare  properly  and  readily  his  shop  drawings  or  other  working  drawings — 
but  no  more;  and  the  preparation  of  shop  drawings  in  the  engineer's  office 
should  be  strictly  avoided.  If  they  are  made  there  so  as  to  suit  the  style  of 
one  shop,  they  would  probably  not  satisfy  the  idiosyncrasies  of  another — 
hence  it  is  better  to  let  each  shop  prepare  its  own  shop  drawings. 

Thirteenth.  It  is  truly  economic  to  use  standard  parts  whenever  this  is 
practicable.  It  saves  time  in  the  office  and  money  in  manufacture. 
Special  sections  of  metal  should  be  avoided,  even  if  they  apparently  be 
economical;  for  generally  time  is  far  more  valuable  than  a  little  extra  metal. 
It  is  only  in  case  of  a  large  amount  of  dupUcation  that  special  sections  are 
legitimate. 

Fourteenth.  A  simple  style  of  lettering  is  both  neat  and  economic,  and 
the  use  of  stencils  and  the  printing  press  involves  the  saving  of  time  and 
money. 

Fifteenth.  No  unchecked  drawing  should  ever  be  allowed  to  go  out  of 
the  office — no  matter  how  pressing  the  call  for  it  may  be.  The  method  of 
checking  all  drawings  should  be  thorough  and  systematic,  and  it  should 
invariably  be  followed. 

Sixteenth.     When  changes  on  drawings  become  necessary,  they  should, 


360  ECONOMICS   OF  BRIDGE WOEK!  CnAPTEa  XXXIV 

of  course,  be  made;  but  their  effects  on  all  parts  should  invariably  be  fol- 
lowed out  to  the  utmost  hmit  of  their  influence. 

Seventeenth.  Handling  of  the  office  work  should  be  done  by  a  thorough 
and  approved  system,  such  as  that  given  on  page  1387  et  seq.  of  "Bridge 
Engineering." 

Eighteenth.  Proper  blank  f onus  facihtate  office  work  and  therefore 
economize  on  cost. 

Nineteenth.  Cost  records  for  the  various  jobs  should  be  kept  so  as  to 
be  able  to  figure  properly  on  the  probable  expense  that  wiU  be  involved  in 
doing  prospective  work. 

Twentieth.  Card  indices  should  be  kept  for  all  possessions  as  well  as 
for  records;  and  this  apphes  to  the  engineer's  library.  No  books  should  be 
taken  from  the  office  without  special  permission,  and  a  record  of  all  such 
loans  should  be  kept  and  utilized  for  compelung  the  return  of  all  books  thus 
borrowed. 


CHAPTER  XXXV 

ECONOMICS  OE  INSPECTION* 

The  economics  of  inspection  is  a  subject  that  is  rather  intangible,  and 
yet  is  a  branch  of  economics  which  really  exists  and  is  of  great  importance; 
hence  it  has  a  proper  place  in  this  general  study,  because  it  involves  a 
desired  result  to  be  accomplished  with  a  mimmum  expenditure  of  effort, 
money,  and  (to  a  slight  degree)  material. 

The  first  point  to  treat  is  this  important  question — To  what  extent  will 
it  pay  the  owner  or  promoter  to  have  his  work  inspected,  and  how  much 
money  should  be  spent  therefor?  To  this  query  the  answer  is  clear  and 
unequivocal,  viz.,  that,  within  the  realm  of  reason,  the  manufacture  and 
construction  of  bridgework  cannot  well  receive  too  thorough  inspection,  and 
the  owner  should  be  wiUing  to  pay  for  it  a  reasonable  compensation  to  high- 
class  men.  A  few  dollars  saved  by  employing  cheap  inspectors  may  mean 
very  many  dollars  lost  through  their  blundering  and  from  lowering  the  value 
of  the  finished  product. 

Like  all  service  functions,  there  should  be  a  strong  distinction  between 
professional  service  at  reasonable  rates  and  simply  commercial  service 
rendered  on  low  competitive  terms.  The  quality  of  inspection  is  evidently 
dependent,  as  is  all  professional  work,  upon  the  character  of  the  men 
employed,  and  this  is  unavoidably  dependent  upon  the  compensation 
allowed. 

From  the  above  it  will  be  appreciated  that  the  quality  of  inspection 
must,  according  to  the  same  rule  as  applies  to  all  business,  be  in  direct  pro- 
portion to  its  financial  reward.  To  be  of  genuine  value,  inspection  must  be 
constant,  intelligent,  and  complete.  A  final  inspection  may  determine  the 
satisfactory  comphance  with  the  contract,  but  cannot,  generally,  secure  an 
adequate  correction  of  errors;  and  certainly  it  cannot  prevent  them  or 
tend  to  the  improvement  of  the  work.  The  criteria  of  quality  of  inspection 
are  the  experience  of  the  men  directly  on  the  job,  the  time  spent  on  it,  and 
the  quaUty  of  the  final  record.  The  engineer  or  person  having  the  respon- 
sibility of  engaging  Inspecting  Engineers  should  decide  upon  the  experience 
and  reputation  of  the  firm  with  which  he  purposes  dealing,  should  know  the 

*  For  a  large  portion  of  the  data  from  which  this  chapter  was  prepared,  the  author 
is  indebted  to  his  friend,  Mr.  Watson  Vredenburgh,  C.  E.,  of  Hildreth  &  Co.,  one  of 
the  best-known  and  most  successful  inspecting  bureaus  of  this  country.  The  first 
part  of  the  chapter,  which  is  his  work,  relates  to  superstructure,  while  the  latter  portion 
from  where  the  treatment  of  substructure  begins  represents  the  author's  opinions. 

361 


362  ECONOMICS   OF  BRIDGEWORK  Chapter  XXXV 

experience  of  the  men  to  be  employed  upon  the  work,  and  should  critically 
examine  the  character  of  both  progress  and  final  reports  furnished  him.  He 
may  also  properly  demand  information  as  to  the  time  of  the  men  employed 
upon  the  job. 

The  method  of  payment  by  tons  inspected  is  satisfactory,  with  a  knowl- 
edge as  to  the  quahty  of  inspection;  but  if  the  Engineer  is  doubtful  as  to  the 
character  of  the  work  that  is  to  be  done,  he  may  arrange  his  terms  on  a 
basis  of  cost  of  the  actual  time  of  the  men  employed  on  the  work,  plus  a 
percentage  or  a  fixed  allowance  per  ton  to  the  Inspecting  Engineers  for 
organization  and  supervision.  It  is  difficult  to  fix  a  proper  charge  per  ton 
to  cover  all  sizes,  kinds,  and  locations  of  work  which  would  be  economical 
to  the  chent  and  fair  to  the  Inspecting  Engineer.  The  latter  may  properly 
make  a  profit  from  the  favorable  combination  of  his  work  at  rolling  mills 
and  manufacturing  shops,  and  from  the  saving  of  time  and  traveling 
expenses,  and  at  the  same  time,  under  proper  arrangement  and  knowledge 
of  these  conditions,  give  the  cHent  the  benefit  of  any  economy  arising  from 
these  propitious  circumstances. 

Some  Engineers,  solely  with  the  false  thought  of  economy  in  the  cost  of 
a  structure,  omit  to  specify  inspection,  or  bow  to  the  wish  of  an  owner  who 
may  consider  the  inspection  an  unnecessary  expense,  without  having  any 
conception  of  either  the  details  of  the  service  or  its  benefits.  It  is  not 
inconceivable  that  an  owner  or  Engineer  who  fails  to  provide  for  the  super- 
vision of  manufacture  may  be  held  responsible  for  damage  or  loss  of  life 
resulting  from  any  failure  during  erection  or  thereafter.  The  question  may 
weU  be  asked— What  is  the  use  of  drawing  plans,  specifications,  and  con- 
tracts, unless  steps  are  taken  to  determine  that  their  requirements  are 
being  carried  out? 

Supervision  of  the  manufacture  of  bridgework  may  be  made  by  the 
direct  employees  of  an  Engineer  or  of  a  Railroad  Company;  and  where  this 
method  may  be  considered,  the  question  of  economy  as  compared  with  the 
employment  of  Inspecting  Engineers  who  make  a  specialty  of  such  work 
becomes  a  factor.  The  reasons  for  the  existence  of  the  latter  class  are 
primarily  that  the  manufacture  of  structural  metalwork  is  conducted  at 
various  rolling  mills  and  at  one  or  more  fabricating  plants,  is  in  progress  at 
several  points  at  the  same  time,  and  is  frequently  intermittent.  If  an 
Engineer  uses  his  own  forces  for  this  work,  it  is  essential  that  a  number  of 
men  be  employed;  and  there  is,  consequently,  much  waste  of  time  and  of 
traveling  expenses.  To  meet  this  situation,  the  independent  Inspecting 
Engineer  establishes  an  organization  of  experienced  men  who  are  per- 
manently located  at  the  various  manufacturing  centers,  and,  by  competent 
supervision  of  their  work,  makes  use  of  their  time  simultancviusly  over  a 
num})cr  of  contracts,  thereby  tending  to  efficiency  and  economy.  The 
overhead  expense  necessary  in  the  operation  and  supeivision  of  inspection 
for  any  single  contract  is  less  with  the  Inspecting  Engineers,  as  their  normal 
expense  of  this  nature  is  distributed  over  a  volume  of  work.    The  efficiency 


ECONOMICS   OP   INSPECTION  863 

of  their  service  can  be  made  at  least  equal  tc  that  of  any  other  Inspectors, 
if  the  principles  of  selection  referred  to  previously  in  this  chapter  are  care- 
fully followed.  The  Inspection  Company,  presumably,  has  a  wide  knowl- 
edge of  shop  methods  and  an  intimate  contact  with  many  shop  managers, 
and  from  experience  is  able  to  handle  the  defects  arising  during  manufacture 
with  some  advantage  of  practical  famiharity,  as  compared  with  the  Design- 
ing Engineer;  and  the  former  has  personal  acquaintance  and  constant 
business  relations  with  the  shop  management  which  the  latter  does  not 
possess. 

Economy  in  Performance 

The  Inspecting  Engineers  entrusted  with  the  mill  and  shop  inspection 
of  the  steel  work  of  any  project  have  directly  the  solution  of  the  problem  of 
accomplishing  the  desired  result  with  the  least  expenditure  of  effort  and 
money  consistent  with  first-class  service. 

I  The  systematizing  of  the  service  for  economical  performance  involves 
the  selection  of  inspectors-in-charge  having  proper  experience  in  the  class 
of  work  under  contract,  as  well  as  training  in  the  handling  of  the  relations 
with  the  manufacturers,  making  correct  reports,  etc.  Where  the  work  is  of 
sufficient  size  and  character  to  warrant  more  than  one  inspector  at  the  shop, 
it  can  be  so  arranged  that  the  assistants  may  be  men  of  lesser  experience, 
with  corresponding  saving  in  remuneration,  and  duties  assigned  to  them 
accordingly.  The  assistants  can  supervise  the  routine  work  of  assembling, 
punching,  and  riveting  before  completion  of  the  finished  members,  and 
cleaning,  painting,  weighing,  and  loading  before  shipment,  besides  estimat- 
ing weights  and  making  proper  reports,  while  the  chief  inspector  can  be 
made  responsible  for  the  relations  with  the  shop,  the  planning  of  the  work 
to  meet  the  field  conditions,  the  delivery  of  material  from  the  mills,  the 
actual  inspection  of  finished  members  for  measurements  and  character  of 
workmanship,  the  shipment  of  material  in  the  order  and  manner  desired  at 
the  building  site,  and  the  making  of  final  reports  to  his  headquarters,  in 
accordance  with  instructions,  so  that  the  client  can  be  furnished  with  a 
complete  descriptive  report  which  will  serve  as  a  valuable  record  of  the 
manufacture. 

Under  a  proper  system  of  organization  there  are  a  number  of  considera- 
tions in  connection  with  the  method  of  inspection  which  should  have  atten- 
tion, in  order  that  the  service  may  be  economical  and  successful.  The 
inspectors  at  both  mills  and  shops  should  be  placed  on  the  work  as  soon  as 
it  starts;  their  instructions  as  to  specifications  and  plans  should  be  prompt 
and  complete;  their  co-operation  with  the  mills  should  be  such  as  to  secure 
the  rolhng  and  shipment  of  material  to  the  shop,  in  accordance  with  the 
order  of  manufacture  there,  so  as  to  prevent  errors  or  discover  defects  as 
early  as  possible  in  the  work,  and  thereby  save  time  in  manufacture  and 
delay  in  shipment,  with  the  additional  advantage  of  avoiding  being  com- 
pelled to  allow  the  work  to  be  patched  by  corrections;  and  the  co-operation 


364  ECONOMICS   OF  BRIDGEWORK  Chapter  XXXV 

should  be  extended  so  as  to  secure  the  cleaning  and  painting  at  the  proper 
time,  and  under  correct  conditions,  in  order  to  save  cost  in  labor,  time,  and 
materials  of  repainting,  either  at  the  shop  or  in  the  field.  The  inspection 
should  cover  such  co-operation  with  the  management  as  to  secure  good 
work  with  the  least  expense  to  the  manufacturer,  and  the  shipment  of 
the  finished  product  at  the  time  and  in  the  order  necessary  for  expeditious 
and  economical  erection. 

Much  that  is  stated  in  Chapter  II,  under  the  heading  "Economics  of 
Mental  Effort,"  is  important  to  apply  to  the  service  of  inspectors  as  well  as 
to  that  of  the  Designing  Engineers.  It  would  be  well  for  the  Inspection 
Firms  and  the  Supervising  Inspectors  to  study  and  practice  the  considera- 
tions referred  to  therein,  and  apply  the  knowledge  gained  to  the  selection 
and  direction  of  their  inspectors  actually  performing  the  duties.  The 
inspectors  should  be  selected  not  only  for  their  experience  but  for  tempera- 
ment to  fit  them  for  the  very  important  duty  of  co-operation  with  manu- 
facturers; also  with  regard  to  their  health  and  habits.  In  all  cases  where 
inspectors  have  demonstrated  their  fitness  and  loyalty  to  the  employer's 
interests,  the  direction  of  the  work  should  be  handled  with  every  considera- 
tion for  the  employee  that  is  consistent  with  the  nature  of  the  work  and 
with  other  conditions  affecting  the  cUents'  interests.  This  relation  between 
Inspecting  Engineers  and  their  employees  in  charge  of  work  affects  directly 
the  character  of  the  service  and,  therefore,  the  economics  of  inspection. 

The  inspection  in  the  field  of  the  placing  of  foundations,  the  building  of 
masonry,  and  the  erection  of  metalwork  needs,  from  an  economic  view- 
point, the  same  consideration  as  does  the  manufacture  of  the  bridge  super- 
structure. The  inspectors  should  be  men  of  experience;  their  duties  should 
be  so  laid  out  as  to  promote  the  progress  of  the  fieldwork,  and  prevent  the 
rejection  and  rebuilding  of  portions  of  the  work;  their  idle  time  should  be 
appUed  to  other  features  of  the  project  when  the  actual  fieldwork  does  not 
demand  their  attention;  and  they  should  be  subject  to  the  same  considera- 
tions of  the  ''Economics  of  Mental  Effort." 

In  general,  it  can  very  properly  be  considered  poor  economy  to  have 
given  attention  to  the  economics  of  promotion  and  secured  competent 
design  and  specifications,  and  not  to  have  provided  for  inspection  to  make 
sure  of  the  entire  manufacture  and  erection  being  performed  in  strict  com- 
pliance with  them;  or  to  have  had  incompetent  inspection  by  persons 
inexperienced  and  without  proper  organization;  or  to  have  failed  to  secure 
a  fair  and  reasonable  compensation  for  Inspecting  Engineers  fully  qualified 
by  experience  and  organization  to  perform  the  required  service  in  a  manner 
commensurate  with  its  importance. 


CHAPTER  XXXVI 

ECONOMICS    OF   SHOPWORK 

Without  the  aid  of  a  thoroughly  posted  bridge-shop  engineer,  it  would 
be  entirely  impracticable  for  anyone  who  is  not  truly  experienced  in  struc- 
tural-steel manufacture  to  write  at  all  intelligently  upon  the  economics  of 
that  branch  of  bridgework.  The  author  encountered  great  difficulty  in 
securing  the  needed  aid,  partially  because  the  work  involved  in  the  prepara- 
tion of  the  notes  called  for  many  hours  of  a  busy  man's  time,  but  mainly 
because  those  who  are  best  posted  on  such  characteristically  practical 
matters  are  not  accustomed  to  express  their  thoughts  on  paper. 

Failure  so  to  collect  one's  knowledge  is  a  serious  drawback  to  any  man; 
for  he  never  can  determine  wherein  that  knowledge  is  hazy  or  lacking  until 
after  he  has  attempted  to  collect,  correlate,  and  systematize  all  that  he 
knows  upon  the  subject  at  issue.  Many  engineers  and  others,  who  in  times 
past  have  done  the  author  the  honor  of  supplying  him  with  special  informa- 
tion, have  afterwards  assured  him  that  they  felt  well  repaid  for  the  time  and 
effort  which  they  had  devoted  to  the  work,  through  their  increase  in  knowl- 
edge obtained  in  making  the  investigation.  Many  a  time  and  oft  in  his 
professional  career  has  the  author  personally  proved  the  correctness  of  this 
principle;  and  he  earnestly  recommends  its  serious  consideration  to  the 
younger  members  of  the  engineering  profession. 

Fortunately  in  this  case,  from  his  old  friend,  Mr.  Thomas  Earle,  C.E., 
Vice-President  of  the  Bethlehem  Steel  Bridge  Corporation,  the  author 
succeeded  in  securing  the  information  of  which  he  was  in  search;  and  he 
feels  very  thankful  for  the  aid  rendered,  because  it  is  certainly  a  great 
concession  and  a  real  favor,  in  the  case  of  an  exceedingly  busy  man,  to  take 
the  trouble  to  collect  and  systematize  the  special  knowledge  which  he 
obtained  by  many  years  of  hard  work.  The  most  of  what  follows  in  this 
chapter  is  essentially  the  substance  of  the  data  so  courteously  furnished  by 
Mr.  Earle. 

The  economics  of  design  to  meet  shop  conditions  has  been  discussed  at 
length  in  Chapter  XXIII;  and  Mr.  Canady's  contribution  thereto  covers 
very  thoroughly  the  ground  of  economics  in  the  drafting-room  of  a  bridge 
shop ;  hence  there  is  left  for  treatment  only  the  economics  of  doing  the  work 
in  the  shops  themselves,  together  with  certain  allied  economic  subjects. 

The  general  economic  problem  in  shopwork  is  to  attain  a  certain  result 
with  the  minimum  expenditure  of  effort,  time,  and  money.     Each  piece  of 

365 


366  ECONOMICS  OF  BRIDGEWORK  Chapter  XXXVI 

material,  therefore,  must  be  taken  up  as  few  times  as  possible  and  carried 
the  shortest  practicable  distance  in  securing  the  desired  results.  A  por- 
tion of  the  problem  must  be  solved  before  any  phj^sical  work  is  performed, 
because  the  design  of  the  shop  will  have  a  large  bearing  upon  it.  The  Con- 
tracting Department  of  the  organization  is  also  an  economic  factor  of  con- 
siderable importance  in  shopwork. 

A  shop  that  is  designed  to  handle  all  classes  of  fabricated  steelwork  will 
not  handle  any  one  particular  class  to  the  greatest  advantage;  hence, 
before  the  shop  layout  is  made,  this  matter  will  have  to  receive  careful 
consideration.  If  a  general  miscellaneous  class  of  fabricated  work  is 
expected,  the  shop  should  be  designed  to  suit  such  mixed  fabrication ;  but 
if  the  circumstances  are  such  that  it  is  probable  that  the  bulk  of  the  manu- 
facture will  be  of  a  particular  character,  it  will  be  advisable  to  design  the 
shop  so  as  to  handle  that  type  of  work  to  best  advantage.  If  that  is  done, 
and  if  the  Contracting  Department  of  the  organization  keeps  the  shop 
filled  most  of  the  time  with  fabrication  of  a  different  class,  the  results  will  be 
unsatisfactory,  thus  proving  the  modus  operandi  to  be  uneconomic.  It  is 
true  that  at  certain  times  it  is  impracticable  to  secure  work  of  the  character 
best  suited  to  the  shop,  and  then  the  results  will  inevitably  be  uneconomic; 
but  it  is  better  to  keep  the  force  occupied  and  everything  moving,  even  at 
a  disadvantage,  rather  than  either  to  close  down  entirely  or  to  let  a  portion 
of  the  men  be  idle.  In  that  case  it  might  eventually  prove  truly  economical 
to  operate  temporarily  at  a  small  pecuniary  loss.  Nothing  in  shop  or  office 
is  so  disheartening  or  so  disorganizing  as  idleness  of  employees;  and  when 
there  is  not  enough  work  on  hand  to  keep  everybody  on  the  qui  vive,  the 
general  effort  slackens  and  the  efficiency  of  the  entire  organization  is  low- 
ered. For  this  reason,  in  bad  times  it  really  pays  to  do  work  at  actual  cost 
or  even  a  trifle  below,  so  that,  when  the  revival  of  business  comes,  all  in  the 
organization  wiU  be  ready  to  tackle  the  new  work  with  energy  and  efficiency. 
If,  during  the  larger  part  of  the  time,  work  of  the  proper  character  is  going 
through  the  shop,  and  if  the  results  are  particularly  favorable,  this  will 
more  than  offset  the  uneconomics  due  to  unsuitable  operation  for  short 
periods. 

The  primary  economic  feature  of  any  shop-layout  is  the  elimination  of 
unnecessary  transportation  and  the  provision  for  rapid  passage  there- 
through of  all  the  materials  which  are  being  fabricated.  The  usual  arrange- 
ment is  to  transport  the  metal  longitudinally  through  on  surface  tracks  and 
to  carry  it  transversely  by  traveling  cranes,  thus  reaching  expeditiously 
every  portion  of  the  floor  space.  In  some  shops  the  cars  are  pushed  along 
the  tracks  by  man  power,  while  in  others  electric  or  gasoline  energy  is 
employed.  In  these  days  of  almost  universal  power  operation  and  of  high- 
priced-labor,  it  certainly  is  economic  to  use  power  for  traction  purposes. 
Of  (;ourse,  the  cranes  are  operated  electrically.  Sonictinies  thoy  are 
handled  by  special  operators  who  ride  on  them,  but  often  by  the  workmen 
on  the  floor  by  means  of  hanging  ropes  arranged  in  a  very  ingenious 


ECONOMICS    OF    SHOPWOKK  367 

manner,  so  as   perfectly   to   control  all  the  operations  of  the  moving 
apparatus. 

Assuming  that  the  work  to  be  fabricated  is  miscellaneous  bridgework, 
including  movable  spans,  there  are  certain  factors  relating  to  major  opera- 
tions and  numerous  others  that  pertain  to  specific  parts  of  the  work;  and 
all  of  them,  according  to  their  effectiveness,  influence  more  or  less  the 
general  economics  of  the  shopwork. 

Principal  Economic  Factors 

The  most  important  factors  covering  all  operations  are  light,  heat,  ven- 
tilation, space,  handling  of  work,  and  management  of  men.  The  first  four 
are,  of  course,  dependent  upon  shop  design;  but  if  they  did  not  receive 
proper  consideration  at  the  time  the  shop  was  planned,  a  study  should  be 
made  in  relation  thereto;  and  any  resulting  proposed  changes  that  promise 
to  provide  more  economic  fabrication  should  be  inaugurated  with  the  least 
possible  delay.  A  relatively  small  amount  of  money  saved  every  day  will 
warrant  the  expenditure  of  a  considerable  sum. 

Similarly,  it  is  truly  an  economic  policy  to  scrap  any  tool,  machine,  or 
apparatus  which  can  be  replaced  by  one  of  decidedly  greater  efficiency,  even 
if  the  one  condemned  be  practically  new.  Economic  results  are  what 
should  be  striven  for,  regardless  of  the  difficulties  and  expenses  that  are 
inevitably  inherent  in  the  making  of  changes.  It  is  this  willingness  of  the 
American  manufacturer  to  scrap  all  apparatus  that  can  advantageously  be 
replaced  by  something  more  effective,  which  has  often  given  him  the 
supremacy  over  his  foreign  competitors.  It  is  the  truly-up-to-date  operator 
who  proves  most  successful  in  his  business. 

Light 

A  well-lighted  shop  is  necessary  to  enable  the  men  to  read  the  drawings 
readily,  to  decipher  the  marks  on  the  metal,  to  find  the  material  expedi- 
tiously, and  to  assemble  it  properly.  Good  light  makes  it  possible  to 
handle  the  metal  rapidly,  to  inspect  the  work  effectively,  and  to  detect 
errors.  It  makes  the  shop  safer  and  more  pleasant  to  work  in ;  and  it  has  a 
beneficial  psychological  effect  upon  the  spirits  of  the  men,  because,  when 
everything  about  the  place  is  bright  and  cheerful,  they  not  only  operate 
to  greater  advantage  but  their  brains  function  better,  with  the  ultimate 
result  of  a  largely  increased  output. 

By  painting  the  interior  of  the  shop  throughout  in  white  and  keeping  the 
paint  comparatively  clean  through  frequent  washings  and  occasional 
renewal,  the  visibility  of  everything  which  it  contains  is  greatly  aug- 
mented, both  in  daylight  and  after  dark,  provided  that  a  proper  system  of 
electric  lighting  is  installed  and  maintained.  It  does  not  pay  to  retain  old, 
dim  lamps;  hence  a  supply  of  fresh  ones  should  be  constantly  on  hand  and 
installed  whenever  necessary.     Moreover,  powerful  lamps  should  always 


368  ECONOMICS  OF  BRIDGEWORK  Chapter  XXXVI 

be  used,  because  the  small  amount  of  electric  cm-rent  saved  by  employing 
weak  ones  is  a  bagatelle  in  comparison  with  the  benefits  obtained  through 
ample  Hghting  capacity. 

Heat 

While  in  the  past  some  bridge  shops  have  been  run  during  the  winter 
months  without  heat,  the  furnishing  of  a  reasonable  amount  of  it  then  will 
assuredly  result  in  a  sufficient  increase  of  tonnage  in  a  given  period  to  pay 
for  several  times  its  cost.  No  man  who  is  uncomfortably  cold  when  housed 
can  work  to  advantage,  although  it  is  true  that  out-of-doors  laborers  in 
winter  often  have  to  keep  busy  in  order  to  maintain  the  necessary  blood 
circulation.  So  much  attention  has  been  paid  in  late  years  to  the  condi- 
tions under  which  labor  operates  that  it  is  probable  that  at  the  present  time 
in  most  of  the  northern  states  it  would  be  impossible  to  induce  men  to  work 
during  the  winter  months  in  an  unheated  shop.  It  is  certain  that  such  a 
shop  would  not  attract  the  best  character  of  labor;  and  efficient  workmen 
are  essential  to  the  production  of  economic  results. 

Ventilation 

In  most  bridge  shops  certain  operations  involve  the  production  of 
considerable  quantities  of  smoke  and  gas;  and  it  is  essential  to  arrange  for 
their  removal  as  rapidly  as  generated.  The  men  cannot  do  satisfactory 
work  unless  they  have  a  sufficient  supply  of  fresh  air;  and  the  atmosphere 
they  breathe  should  be  free  from  gases  and  odors.  Even  though  these  be 
not  actually  harmful,  their  existence  militates  against  economy;  because, 
when  such  odors  are  perceptible,  the  workmen  seem  to  get  the  impression 
that  all  of  their  ordinary  ills  and  discomforts  result  therefrom.  The 
importance  of  ventilation  is  greater  where  the  design  of  the  shop  is  such  that 
overhead  traveling  cranes  are  operated  by  men  located  near  the  roof,  as 
the  heat,  smoke,  and  gases  accumulate  there  and  make  it  impossible  for 
these  men  to  handle  their  work  properly. 

Space 

The  shop  should  be  so  designed  that  all  of  the  work  of  any  particular 
character  can  be  done  in  a  space  by  itself;  and  sufficient  area  should  be 
provided  for  handling  the  maximum  output  of  material  for  each  oj^eration 
throughout  the  shop.  For  instance,  if  the  space  devoted  to  reaming  be 
insufficient,  the  shop  up  to  that  point  will  become  over-crowded  with 
material  ready  for  reaming,  the  shop  beyond  will  not  contain  sufficient 
material,  and  the  tonnage  of  the  work  going  through  will  be  limited  because 
of  the  lack  of  space  in  this  particular  area.  It  is  just  as  important  to  have 
enough  space  for  each  operation  as  it  is  to  have  sufficient  total  space.  If 
it  be  found  that  there  is  a  lack  of  space  in  certain  areas,  and  if  more  space 
cannot  be  secured  at  these  points,  the  trouble  will  have  to  be  overcome  as 


ECONOMICS    OF   SHOPWORK  369 

much  as  possible  by  placing  particularly  efficient  men  in  these  areas  and  by 
making  special  efforts  to  prevent  their  work  from  being  delayed  by  the 
other  operations.  Material  must  be  ready  for  them  as  soon  as  they  can 
handle  it,  and  it  must  be  taken  away  from  them  as  soon  as  they  have 
finished  with  it.  This,  of  course,  involves  some  increase  in  expense,  but 
the  additional  tonnage  secured  in  a  given  time  will  amply  warrant  the 
extra  cost. 

Handling  of  Work 

The  four  factors  of  light,  heat,  ventilation,  and  space,  all  dependent 
upon  shop  design,  have  a  direct  bearing  upon  the  proper  planning  of  the 
passage  of  the  work  through  the  shop.  A  proper  planning  system  is  one  of 
the  most  important  factors  in  shop  economics;  and  certainly  it  would  not 
work  out  satisfactorily,  unless  there  were  sufficient  hght,  heat,  ventila- 
tion, and  space.  Such  a  system  should  provide  for  the  location  and  move- 
ment of  the  material  from  the  time  it  is  delivered  at  the  shop  until  the  time 
it  is  shipped  therefrom.  The  Shop  Manager  should  always  be  able  to 
ascertain  immediately  in  exactly  what  portion  of  the  shop  any  particular 
material  is  located.  Special  stress  should  be  laid  upon  the  importance  of 
having  ample  space  for  the  raw  materials  as  they  are  received  from  the 
mills.  Some  years  ago  this  was  neglected,  resulting,  in  the  case  of  large 
shops,  in  unsatisfactory  operation,  as  it  was  impossible  to  locate  and  bring 
into  the  shop  any  particular  material  on  short  notice. 

There  is  an  ideal  -feature  of  economics  in  shop  practice  that  should  be 
adhered  to  when  it  is  possible,  viz.,  the  continuous  passage  of  all  material 
in  one  direction  through  the  shop.  This  is  not  always  feasible;  but  it  is 
the  general  experience  that,  whenever  the  principle  is  violated  by  carrying 
material  backward,  progress  is  interfered  with,  output  is  lessened,  and  unit 
cost  of.  production  is  increased. 

Management  of  Men 

The  efficient  management  of  the  workmen  is  one  of  the  most  important 
factors  in  shop  economics;  because  the  maximum  of  output  can  only  be 
attained  by  having  each  man  in  the  shop  labor  to  his  limit  of  efficiency,  all 
work  together  harmoniously,  and  all  act  in  concert  under  a  scientifically- 
laid-out  programme. 

If  workmen  are  to  develop  one  hundred  per  cent  of  efficiency,  or  any- 
thing like  that  amount,  they  must  be  well  fed,  properly  housed,  com- 
fortable in  their  surroundings,  happy,  interested  in  their  occupation,  con- 
tented with  their  recompense,  and  amused  in  their  leisure  hours.  Some  of 
the  broad-gauge  managers  of  bridge  shops  are  recognizing  these  require- 
ments, and  are  endeavoring  to  fulfil  them  in  various  ways.  For  instance, 
cafeterias  are  being  established  for  the  employees,  where  good,  plain,  whole- 
some food  is  served  at  actual  cost;  Hbraries  and  reading  rooms  are  being 


370  ECONOMICS   OF  BRIDGEWORK  Chapter  XXXVI 

provided;  comfortable  cottages  with  all  modern  improvements  are  being 
built  and  rented  to  the  men  at  low  rates;  playgrounds  are  being  inaugu- 
rated; and  opportunities  for  large  earnings  are  being  afforded  by  the 
adoption  of  the  system  of  piece-work.  If  a  method  of  annual  profit-sharing 
hke  that  advocated  by  the  author  and  expounded  in  Chapter  XXXIII 
were  adopted,  in  addition  to  the  other  welfare  methods  just  mentioned, 
most  of  the  labor  troubles  in  bridge  shops  would  disappear.  Great  care 
should,  however,  be  exercised  in  giving  the  employees  unusual  privileges  or 
rewards,  as  these  may  do  more  harm  than  good  if  the  employee  does  not 
feel  that  they  are  due  to  special  effort  and  that  he  is  receiving  them  as  a 
payment  for  work  that  he  has  performed.  There  has  recently  been  too 
much  talk  for  rights  without  consideration  of  duties.  Rights  result  only 
from  the  performance  of  duties.  It  is  most  important  in  the  interest  of 
true  economy  that  the  amount  of  each  workman's  compensation  shaU  be 
proportionate  to  the  efficiency  of  his  accomphshment.  A  flat  scale  of 
wages  is  absolutely  destructive  to  progress,  output,  initiative,  and  economy. 

Safety  Considerations 

Every  effort  made  by  both  the  management  and  the  employees  to 
increase  the  safety  of  the  workmen  is  a  step  in  the  line  of  true  economy. 
Each  accident  in  the  shop,  no  matter  how  trivial,  causes  immediately  more 
or  less  delay,  and  often  incapacitates  one  or  more  men  for  some  time. 
Notwithstanding  the  fact  that  such  men  may  be  replaced  quickly,  their 
successors  naturally,  for  a  while  at  least,  are  not  as  efficient;  hence  progress 
is  impeded  by  the  failure  of  the  new  men  to  function  effectively. 

Again,  many  of  the  injured  men  return  to  their  work  out  of  condition — 
some  of  them  permanently  so,  for  instance  with  the  loss  of  a  finger  or  an 
eye.  Then  there  must  be  considered  living  expenses  and  doctor's  bills 
during  the  enforced  absence  from  work.  Somebody  has  to  pay  these;  and 
while  in  the  end  they  are  borne  by  society,  they  are  carried  primarily  by  the 
shop ;  and  that  shop  which  is  freest  from  accidents  has  the  least  expense  on 
that  account.  Other  things  being  equal,  it  can,  therefore,  secure  the 
largest  percentage  of  profit.  Generally,  too,  the  workman  has  to  be  com- 
pensated for  his  injury,  which  is  another  economic  factor  of  importance. 
Possibly,  insurance  will  cover  this;   but  often  the  company  has  to  pay  it. 

Much  might  be  said  from  the  humanitarian  point  of  view  concerning  the 
prevention  of  accidents;  but  this  is  a  treatise  on  economics,  not  ethics. 
Viewed  from  every  possible  angle,  it  is  in  the  line  of  true  economy  for  the 
company  to  take  every  precaution  to  prevent  accidents  in  the  shop;  for 
safety  and  efficiency  are  inseparable.  To  this  end  the  responsibility  should 
be  laid  upon  one  of  its  officers  whose  duty  it  would  be  to  anticipate  all 
possible  accidents  in  the  shop  and  take  measures  to  prevent  their  occur- 
rence. This  could  b(^  accomplished  in  various  ways,  among  which  might 
be  mentioned  the  following: 


ECONOMICS    OF    SHOPWORK  371 

A.  Properly  guarding  the  running  parts  of  all  machinery. 

B.  Frequent  inspection  of  all  machines  of  which  the  failure  could 
injure  anybody. 

C.  Modification  of  machinery  that  is  essentially  dangerous  in  any 
particular. 

D.  Posting  of  efficient  warnings  around  the  buildings,  calling  attention 
to  possible  dangers. 

E.  Keeping  the  floors  clean  so  that  they  will  not  become  slippery. 

F.  Prevention  of  excessive  or  injurious  dust  in  the  atmosphere  of  the 
shop. 

G.  Occasional  lectures  to  the  workmen  instructing  them  as  to  what 
they  should  do  to  avoid  accidents. 

H.  Distribution  of  pamphlets  treating  of  important  matters  of  safety, 
sanitation,  hygiene,  and  like  subjects. 

I.  Having  available  at  all  times  a  surgeon  to  care  for  anyone  who, 
in  spite  of  all  precautions,  may  be  injured. 

Smoking* 

Smoking  in  the  shop,  for  several  good  reasons,  is  an  uneconomic  practice 
and  should  never  be  permitted.  In  the  first  place,  it  causes  danger  from 
fire;  in  the  second,  it  occupies  a  quite-considerable  portion  of  employees' 
time  that  should  be  devoted  to  work;  and  in  the  third,  no  man's  mind  can 
act  as  keenly  when  his  system  is  under  the  soporific  influence  of  nicotine  as 
it  can  when  free  from  the  effects  of  that  narcotic.  Very  few  first-class 
shops  nowadays  permit  smoking  on  the  premises.  The  restrictions  against 
smoking  apply  with  even  more  force  in  the  drafting-room  than  they  do  in 
the  shop;  for,  in  addition  to  the  objections  just  noted,  it  might  pertinently 
be  stated  that  the  dropping  of  hot  ashes  from  cigarettes  onto  tracing  cloth 
is  not  specially  conducive  to  economy.  If  a  man  must  smoke,  let  him  do  it 
out  of  working  hours  and  not  upon  the  company's  premises,  unless  there  be 
provided  a  smoking  room  for  use  during  the  luncheon  hour  and  after  one's 
day's  work  is  done. 

Anticipating  Troubles 

All  officials  of  the  company  should  make  it  their  business  to  try  in  every 
possible  manner  to  anticipate  and  forestall  accidents  or  occurrences  of  any 
kind  tending  to  interfere  with  shop  operations  or  to  reduce  efficiency, 
quality  of  workmanship,  or  output.  Conferences  of  officials  should  be 
held  from  time  to  time  for  the  purpose  of  discussing  this  and  other  matters 
relating  to  the  general  welfare  of  the  works  and  the  workmen. 

*  Mr.  Earle  deems  the  author  to  be  a  bit  drastic  in  his  views  on  the  uneconomics 
of  smoking. 


372  ECONOMICS   OF  BRIDGEWOKK  Chapter  XXXVI 


Standardization  * 

There  are  few  matters  of  such  importance  for  efficiency  and  economics 
as  that  of  standardization ;  and  it  should  apply  not  only  to  tools  and  prod- 
uct but  also  to  the  operations  of  the  workmen.  The  motion-stud}^  expert 
has  proved  conclusively  that  everybody  wastes  a  certain  portion  of  his  time 
and  energy  in  all  of  his  operations;  hence  it  would  be  economic  to  make  a 
study  of  all  workmen's  motions  and  indicate  to  them  what  they  should  do 
in  order  to  correct  at  least  the  most  glaring  of  such  faults.  This  has  alread}^ 
been  tried;  and  the  good  results  effected  have  been  surprising.  Probably 
the  motion-study  expert  who  secures  the  best  results  is  the  foreman  who  sees 
that  the  men  learn  how  to  do  their  work  without  loss  of  motion,  and  then 
treats  them  in  such  a  manner  as  will  make  them  wish  to  stay  where  they 
are. 

Stock  Materials 

The  amount  of  stock  material  that  is  kept  on  hand  is  one  of  the  deter- 
mining factors  in  the  size  of  space  required.  It  is  influenced  by  the  char- 
acter of  the  work  done,  and  is  dependent  upon  whether  a  warehouse  supply 
of  material  is  promptly  available.  If  quick  shipments  are  to  be  made  and 
high  prices  obtained  for  them,  a  considerable  amount  of  stock  material  will 
have  to  be  kept  on  hand ;  and  it  should  be  stored  under  shelter  so  as  to  be 
protected  from  rusting.  A  day  is  coming,  and  it  may  not  be  far  distant, 
when  the  purchaser  of  a  bridge  will  insist  that  the  structure  shall  be  manu- 
factured of  metal  which  has  never  been  attacked  seriously  by  rust  or  has 

*  Concerning  this  clause  and  the  next  succeeding  one,  Mr.  Earle  has  commented 
by  letter  as  follows: 

I  wish  to  comment  somewhat  on  what  you  say  under  the  above  heading,  in  connec- 
tion with  what  3'ou  say  under  the  heading  of  Stock  Materials.  The  question  of  Standard- 
ization as  relating  to  economy  of  shopwork  is,  of  course,  the  smaller  portion  of  the 
economy  of  Standardization ;  for,  so  long  as  each  engineer  wishes  his  bridges  built  to  his 
own  specification  and  design,  it  would  be  uneconomical  for  the  Shop  to  store  steel  under 
cover.  It  is,  to  my  mind,  absolutely  undefensiblc  for  standard  bridges  of  standard  lengths 
to  be  built  in  accordance  with  the  various  specifications,  as  is  now  being  done.  Deck 
plate-girder  spans,  through  [)Iatc-girdcr  spans,  and  truss  spans  of  two  or  three  types  can 
be  built  to  standard  specifications  and  standard  loading  and  will  give  absolutely  as  good 
service  on  the  New  York  Central  R.R.  as  they  will  on  the  Pennsylvania  R.R.  or  on  the 
Chicago  &  Northwestern  R.R.,  or  any  other  railroad;  and,  as  far  as  wc  can  tell  at  the 
present  time,  the  life  of  a  bridge  under  one  good  specification  is  the  same  as  the  life  of  a 
similar  bridge  under  another  good  specification.  If  all  such  bridges  were  built  in  accord- 
ance with  a  standard  design  and  sf)ecification,  it  might  then  be  economical  for  the 
Bridge  Shop  to  keej)  material  for  su(!h  structures  under  cover.  The  manufacturers 
would  then  know  that  it  would  be  safe  to  do  this;  for,  if  they  did  not  sell  to  one  cus- 
tomer, they  could  sell  to  another.  Incidentally,  this  would  lie  a  great  advantage  to 
customers;  because,  if  they  should,  want  a  bridge  in  a  great  hurry  on  account  of  a 
flood  or  other  accident,  it  could  undoubtedly  be  secured  without  delay  from  a  shop 
having  such  a  bridge  in  process  of  manufacture. 


ECONOMICS    OF    SHOPWORK  373 

been  stored  or  kept  for  any  length  of  time  in  any  place  unprotected  from  the 
weather. 

Stock  material  should  be  ordered  to  such  specifications  as  will  permit  of 
its  employment  in  connection  with  the  usual  class  of  work  going  through 
the  shop.  Each  metal  section  should  be  kept  by  itself;  and  the  various 
lengths  thereof  should  be  stored  in  separate  piles.  The  storage  ground 
should  be  divided  into  various  areas;  and  records  should  be  kept  of  the 
location  of  the  materials  in  these  areas.  It  is  only  in  this  way  that  the  Con- 
tracting Department  would  be  warranted  in  promising  early  shipment,  in 
order  to  secure  orders  at  favorable  prices.  It  is  essential  for  the  satis- 
factory and  economical  running  of  the  shop  that  both  stock  materials  and 
contract  materials  can  be  deHvered  promptly  to  the  machines  as  soon  as  it 
is  decided  to  call  for  them. 

In  the  case  of  special  material  for  contracts,  just  as  soon  as  it  is  received 
from  the  mills  it  should  be  stored  in  the  units  in  which  it  is  later  to  be 
brought  into  the  shop,  the  said  units  being  the  metal  called  for  by  a  bill 
of  material,  or  shown  on  a  drawing,  or  indicated  by  some  combination  of 
these  methods.  A  record  should  be  kept  of  its  location,  so  that,  when  the 
templets  are  completed  and  the  shop  is  ready  to  take  up  the  work,  it  can  be 
delivered  in  complete  units;  and  it  should  then  be  carried  through  the  shop 
in  such  units.  Too  much  stress  can  hardly  be  laid  upon  the  desirabUity  of 
bringing  in  material  complete  in  units,  as  the  lack  of  any  portion  thereof 
would  hold  up  in  the  shop  a  large  part  of  the  balance  of  the  material  of  this 
particular  unit;  and  this  material  would  clog  up  the  shop  and  either  pre- 
vent other  material  from  going  through  or  allow  it  to  pass  only  at  additional 
cost. 

Supply  of  Labor 

For  several  years  past  the  supply  of  suitable  labor  for  fabricating  shops 
has  been  limited;  and  there  is  no  reason  to  assume  that  there  will  soon 
be  any  improvement  in  this  respect — in  fact  the  evidence  at  the  present 
time  is  to  the  effect  that  the  difficulties  will  be  aggravated  rather  than 
ameliorated;  and  this  condition  must  receive  due  thought  in  considering 
shop  economics.  The  character  of  the  shop  and  the  way  in  which  the  work 
goes  through  it  have  an  important  bearing  upon  the  securing  of  a  sufficient 
force  of  capable  employees. 

It  is  of  the  utmost  importance  that  a  permanent  force  of  well-trained 
workmen  be  estabhshed.  Every  legitimate  effort  should  be  made  to  retain 
the  services  of  capable  and  efficient  workmen,  because  the  breaking  in  of 
each  new  man  costs,  in  various  ways,  considerable  money.  There  is  an 
immense  difference  between  both  the  quality  and  the  quantity  of  the  daily 
accomphshment  of  the  trained  workman  and  that  of  one  who  is  not  experi- 
enced. As  one  walks  through  a  bridge  shop,  even  on  a  short  visit,  by 
watching  for  a  few  minutes  the  men  at  work  he  can  readily  distin^ish 
between  those  who  are  experienced  and  those  who  are  not;  and  when  a  new 


374  ECONOMICS   OF   BRIDGEWORK 

shop  is  opened  with  imtraiQed  workmen,  it  takes  many  months  to  bring  it 
into  any  condition  at  all  approaching  the  ideal. 

Tool  Equipment 

A  comparatively  large  expenditure  is  warranted  for  securing  labor-sav- 
ing tools.  Labor  is  a  very  undependable  element;  but  the  tools,  if  given 
proper  attention,  wiU  take  care  of  the  work  at  all  times.  In  the  case  of 
shops  of  equal  capacity,  the  difficulties  of  running  them  successfully  seem  to 
increase  about  in  proportion  to  the  square  of  the  number  of  men  employed. 

Shop  Floors 

The  character  of  the  shop  floors  has  an  influence  on  production,  because 
it  has  an  effect  on  the  character  of  the  labor  that  can  be  secured  and  also 
upon  the  amount  of  work  that  can  be  performed  in  a  given  time.  The 
floors  should  be  level,  clean,  in  good  repair,  and  not  too  hard.  A  wood- 
block floor  seems  to  meet  these  conditions,  as  it  can  be  kept  clean  and  level, 
is  not  too  hard,  is  long  lived,  and  can  be  repaired  quickly  and  economically. 
It  is  not  cold,  and,  when  kept  clean,  it  is  not  shppery. 

Straightening  Metal 

A  certain  amount  of  material  as  it  comes  from  the  mills  is  not  sufficiently 
straight  to  be  used  in  the  condition  in  which  it  is  received,  if  the  result  is  to 
be  a  first-class  product.  Straightening  by  hammers  is  unsatisfactoiy  and 
expensive,  and  it  is  prohibited  by  many  specifications.  The  best  results 
can  be  secured  by  the  installation  of  straightening  roUs  for  plates  and 
angles  and  roUs  or  presses  for  channels  and  I-beams. 

Marking  Metal 

The  marking-off  of  the  material  is  largely  done  by  hand;  and  efficient 
appliances  should,  therefore,  be  provided  for  handling  and  holding  the 
individual  pieces.  Jib-cranes  or  traveling  wall-cranes  are  suitable  for 
such  manipulation.  They  should  have  either  electric  or  quick  air  hoists, 
and  should  be  operated  from  the  floor.  Overhead  cranes  should  be  pro- 
vided for  delivering  materials  to  the  proper  zone  and  for  removing  them 
therefrom.  Proper  skids  should  be  furnished  on  which  the  material  can 
be  marked  off  and  stored. 

Trimming  and  Cutting 

As  trimming  and  cutting  of  metal  in  the  condition  in  which  it  comes 
from  the  mill  aie  always  required,  the  necessary  space  and  tools  should  be 
provided  for  doing  this  work  either  before  the  material  is  marked  off  or 
before  it  is  punched.     Among  the  tools  that  might  be  mentioned  are 


ECONOMICS    OF    SHOPWORK  375 

angle,  beam,  and  plate  shears;  coping  machines  for  coping  I-beams  and 
channels;  planers  for  trimming  the  edges  of  plates;  planing  or  milling 
machines;  and  machines  for  ending  stiff eners  and  chamfering  them  so  as  to 
fit  the  flange  angles.  Planing  or  chamfering  machines  can  be  designed  with 
one  head  fixed  and  one  movable,  so  as  to  permit  the  setting  of  the  heads  a 
given  distance  apart,  whereby  both  ends  of  a  nmnber  of  stiffeners  can  be 
chamfered  at  one  setting,  and  all  the  duplicate  pieces  chamfered  while  the 
heads  are  a  given  distance  apart. 

Punching 

In  punching,  the  material  has  to  be  handled  in  individual  pieces.  Jib- 
cranes  or  traveling  wall-cranes  should,  therefore,  cover  the  tool  area;  and 
overhead  cranes  should  be  provided  for  transferring  the  material  to  and 
from  the  punches  in  quantities.  As  an  alternative,  facilities  for  trucking 
the  said  material  in  quantities  might  be  provided.  Punches,  to  as  great  an 
extent  as  possible,  should  be  equipped  with  spacing-tables  of  some  of  the 
various  standard  designs;  and,  where  practicable,  the  punching  should  be 
done  by  spacing  machines.  The  cost  of  punching  a  given  number  of  holes 
is  reduced  thereby,  the  marking-off  of  the  material  is  eliminated,  and,  in 
most  cases,  the  cost  of  templet-making  is  diminished.  It  is  also  possible  to 
punch  a  larger  number  of  holes  within  a  given  time;  and  the  increase  in 
capacity  of  the  Punch  Shop  would  make  spacing-punches  economical,  even 
if  the  actual  cost  of  doing  the  work  were  the  same.  In  addition  to  this,  as  a 
rule,  the  work  is  more  accurate,  which  condition  militates  for  economy,  in 
that  the  fitting-up  is  facilitated. 

It  is  probable  that  more  small,  labor-saving  devices  have  been  intro- 
duced in  Punch  Shops  than  in  any  other  part  of  the  fabricating  plant — 
such,  for  instance,  as  electrically-operated  gags,  ball  tables,  punching 
through  wooden  or  pasteboard  templets,  using  a  model  and  applying  the 
principle  of  the  pantagraph,  etc. 

Drilling 

Many  bridge  specifications  require  metal  of  over  a  certain  thickness  to 
be  drilled  instead  of  punched;  and  often  such  drilling  really  proves  to  be 
more  economical  than  the  punching.  The  shop,  therefore,  that  is  going  to 
handle  heavy  bridge  work  has  to  have,  in  addition  to  its  punching  equip- 
ment, a  sufficient  number  of  power  drills  to  permit  the  drilling  from  the 
solid  of  a  considerable  tonnage  of  metal.  If  the  shop  is  designed  especially 
for  this  class  of  work,  sufficient  drills  should  be  provided  to  handle  from 
fifty  to  seventy-five  per  cent  of  the  normal  output  of  the  shop.* 

*  The  author  predicts  that  it  will  not  be  many  years  before  all  important  steel 
bridgework  will  be  drilled  solid,  and  that  the  increased  cost  of  so  doing  will  amount 
practically  to  zero. 


376  ECONOMICS   or  BRIDGEWORK  Chapter  XXXVI 

Storage  of  Punched  Metal 

As  it  is  not  possible  in  a  shop  handling  a  large  tonnage  to  punch  or  drill 
all  of  the  material  for  a  particular  unit  at  the  same  time,  sufficient  space 
should  be  provided  in  the  Punch  Shop,  or  the  Assembling  Shop,  or  between 
them,  for  the  storage  of  punched  or  drilled  material,  so  that  when  the 
Assembling  Shop  is  ready  to  start  on  the  assembUng  of  a  given  unit,  or 
any  part  thereof,  the  metal  can  be  located  and  delivered  to  the  assemblers  as 
wanted. 

Assembling 

The  planning  system  should  also  provide  for  the  performance  of  second- 
ary operations,  if  necessary,  before  the  dehvery  of  the  material  to  the 
Assemblers.  Angles,  plates,  etc.,  frequently  have  to  be  bent  before  or  after 
punching,  and  sheared  edges  of  plates  have  to  be  planed;  and  the  assem- 
bUng work  should  not  be  held  up  by  any  of  these  operations. 

As  the  assemblers  handle  the  material  in  mill  sizes,  they  require  cranes 
for  the  rapid  manipulation  and  holding  of  same  while  assembling.  These 
cranes  should,  preferably,  be  operated  from  the  floor.  Overhead  cranes 
should  be  provided  for  handling  the  finished  pieces.  The  assembling  area 
should  be  equipped  with  level  skids  at  such  a  height  above  the  floor  as  to 
permit  of  accurate  and  rapid  assembling.  It  is  important  that  the  skids  be 
truly  level,  so  that  the  material  assembled  thereon  will  be  straight  and  out 
of  wind. 

If  girders  are  assembled  in  a  vertical  position,  cast-iron  bases,  or  some- 
thing similar,  should  be  provided  for  holding  them  during  the  assembling. 
These  bases  should  be  of  such  a  character  that  the  bottom  flanges  of  the 
girders  can  be  readily  clamped  thereto,  in  order  to  prevent  the  girders  from 
falling  over.  The  tops  of  the  bases  should  be  at  the  same  elevation ;  and, 
if  the  girders  are  to  be  cambered,  steel  filling-pieces  can  be  placed  above  the 
bases,  so  as  to  provide  the  camber  desired.* 

Reaming 

Present-day  specifications  for  bridgework  provide,  in  the  case  of  a  large 
portion  of  the  work,  that  the  rivet  holes  shall  be  reamed  after  assembling. 
This  requirement  renders  necessary  the  furnishing  of  a  complete  reaming 
equipment;  and,  in  the  end,  economy  will  result  if  the  reaming  capacity  is 
sufficient  to  take  care  of  the  entire  output  of  the  shop.  Even  though  the 
specifications  do  not  require  it,  economy  will  result  from  the  reaming  of  all 
rivet  holes  after  assembling.  The  reamers  should  be  power-driven  and 
capable  of  being  forced  up  to  the  capacity  of  the  drills. 

Level  skids  should  be  furnished  in  the  reaming  area  on  which    the 

*  The  author  dooms  the  cainberiiiff  of  phdo-girders  to  bo  absohitcly  unnecessary 
and,  conscfjuently,  uneconomic. 


ECONOMICS    OF    SHOPWORK  377 

material  can  be  reamed,  and  on  which  it  can  be  stored  so  as  to  remain 
straight  and  out  of  wind.  Overhead  travehng  cranes  should  be  provided 
for  conveying  the  material  to  and  from  the  reamers. 

Riveting 

Rivets  should  be  driven  as  much  as  possible  by  power  machines;  and 
machines  of  different  types  should  be  provided,  in  order  to  be  able  to  drive 
the  greatest  number  of  rivets  practicable.  These  machines  should  have 
ample  power,  because  tight  rivets  should  be  secured  throughout  the  work 
the  first  time  they  are  driven,  the  expense  of  cutting  out  and  redriving 
rivets  being  thereby  reduced  to  a  minimum.  Portable  riveting  machines 
probably  give  the  best  results,  as  it  is  more  economical  to  move  a  compara- 
tively light  riveting  machine  than  it  is  to  shift  a  heavy  piece  of  bridgework. 
Machines  can  be  quickly  handled  and  the  rivets  can  be  rapidly  driven,  if 
the  machine  is  suspended  from  a  wall-crane  or  a  jib-crane.  These  cranes 
can  be  operated  from  the  floor  by  one  of  the  riveting  gang.  The  bridge 
members  can  be  transferred  by  travehng  wall-cranes,  overhead  cranes,  or 
trucks. 

Milling  and  Planing 

Certain  members  of  trusses,  columns,  and  sometimes  even  girders  have 
to  have  their  ends  planed;  and  various  machines  have  been  built  for  this 
work,  a  rotary  planer  being  generally  the  most  economical.  Milling 
machines,  however,  have  been  used.  No  matter  which  type  of  machine  is 
employed,  economy  will  result  by  having  it  furnished  with  two  heads,  one 
of  which  travels  on  the  ways  of  the  apparatus.  This  permits  the  heads 
to  be  set  at  a  given  distance  apart,  and  both  ends  of  the  piece  to  be  planed  or 
milled  at  the  same  time,  duplicate  pieces  being  finished  without  re-setting 
the  movable  head. 

Boring 

Double-headed  horizontal  or  vertical  boring  machines  should  be  pro- 
vided with  one  head  traveling  on  the  ways  of  the  machine,  so  that  the  pin 
holes  can  be  bored  at  an  exact  distance  apart.  For  duphcate  parts  there 
wUl  be  no  need  of  re-setting  the  heads. 

Special  Space 

All  bridge  members  do  not  need  to  go  through  the  same  number  of  opera- 
tions in  order  to  be  completed ;  and  some  provision  should,  consequently, 
be  made  for  keeping  material  that  requires  only  one  or  two  operations 
(or  special  operations)  out  of  the  Main  Shop.  To  this  end  a  special  space 
should  be  provided  for  the  fabrication  of  shoes,  cross-frames,  laterals,  small 
struts,  and  other  miscellaneous  pieces. 


378  ECONOMICS   OF   BRIDGEWORK  Chapter  XXXVI 

Machine  Shop 

For  the  fabrication  of  fixed  spans  not  many  machinB  tools  are  required, 
the  turning  of  pins,  the  planing  of  main  members,  shoes,  and  base  plates, 
and  the  boring  and  drilling  of  holes  being  about  the  only  machine  opera- 
tions required.  If,  however,  movable  spans  are  to  be  manufactured,  a 
small  machine  shop  will  effect  an  economy  of  operation.  Such,  a  machine 
shop  should  be  equipped  with  the  following  tools: 

Boring  Mill, 
Grinding  Machine, 
Lathe, 

Screw  Cutter, 
Planing  Machine, 
Slotting  Machine. 

Foundry 

It  is  probable  that  an  iron  or  steel  foundry  cannot  be  added  to  the 
equipment  of  the  fabricating  plant  with  economy,  unless  there  is  a  market 
for  general  commercial  work;  because  there  are  not  enough  castings 
required  in  bridgework  to  keep  a  foundry  busy  more  than  a  very  small 
portion  of  the  time. 

Blacksmith  Sho'p 

A  Blacksmith  Shop  should  be  installed  with  hammers,  presses,  heating 
furnaces,  etc.  If  the  Shop  is  one  of  large  capacity,  there  should  be  added  a 
rivet-and-bolt-making  plant  with  the  necessary  heating  furnaces,  continu- 
ous rivet-making  machines,  bolt  machines,  screw-cutting  machines,  and 
bins  for  the  storage  of  rivets  and  bolts. 

Shop  Assembling 

Bridge  specifications  in  many  cases  provide  that  the  members  of  riveted 
trusses  shall  be  assembled  at  the  shop,  that  the  field  holes  shall  be  reamed 
while  the  trusses  are  so  assembled,  and  that  the  members  shall  be  match- 
marked  before  they  arc  taken  apart.  This  ensures  the  proper  matching  of 
the  holes  when  the  work  is  subsequently  erected.  The  shop,  therefore, 
should  have  the  necessary  space  and  equipment  for  assembling  such  trusses. 
Generally,  it  is  economical  rather  than  the  reverse  to  do  such  assembling 
and  reaming;  but,  if  there  be  a  large  number  of  duplicate  spans,  it  is 
uneconomical.  In  such  a  case  the  field  connections  should  be  reamed  to 
iron  templets,  so  that  the  members  will  be  interchangeable.  The  woi-k  can 
•be  done  mu(;h  more  quickly  in  this  way;  and,  if  it  be  carefully  performed, 
the  results  will  always  be  satisfactory.  If  desired,  one  or  two  of  the  trusses 
can  be  assembled  before  any  of  them  are  shipped,  in  order  to  check  the 
accuracy  of  the  work. 


ECONOMICS    OF    SHOPWORK  379 

If  possible,  the  space  for  such  assembling  of  trusses  should  be  com- 
manded by  overhead  traveling  cranes,  and  should  be  equipped  with  port- 
able power  drills,  both  horizontal  and  vertical.  These  portable  drills  will 
be  found  of  great  value  in  the  shop  as  a  supplement  to  the  regular  drilling 
and  reaming  equipment.  The  top  and  bottom  chords  of  the  trusses,  after 
planing,  should  be  assembled  in  the  shop,  and  the  holes  on  one  side  of  the 
sphce  drilled  from  the  soHd  whilst  the  chords  are  thus  assembled,  using 
these  portable  drills. 

Painting 

For  finishing  and  painting,  ample  space  and  proper  handling  facilities 
should  be  provided.  At  least  a  portion  of  the  space  (and  the  larger  the 
better)  should  be  covered,  as  all  of  this  work  cannot  be  done  out  of  doors 
during  the  winter.  While  spraying  machines  have  been  used  for  painting, 
doing  the  work  by  hand  seems  to  give  more  satisfactory  results. 

Tracks 

Ample  track  facilities  should  be  provided  both  for  the  bringing  in  of 
material  to  the  shop  and  for  shipping  it  out. 

Templet  Shop 

For  economy,  the  templet  shop  should  be  light,  well  heated,  and 
furnished  with  benches  at  one  level,  and  with  tools  for  planing,  cutting, 
and  boring  the  templet  lumber  and  for  boring  and  shearing  pasteboard  for 
templets.  The  use  of  the  latter  material  instead  of  lumber  is  in  the  line 
of  true  economy. 

Recapitulation 

To  summarize — the  main  factors  are  light,  heat,  ventilation,  space,  and 
tools;   and  the  Planning  System  should  result  in: 
Availability  of  material  when  desired. 
Short  and  continuous  travel. 
Handling  as  few  times  as  possible. 
Keeping  of  men  busy. 
Tools  of  such  character  as  to  permit  the  securing  of  the  proper  grade 

of  workmanship. 
Competent  employees  to  maintain  such  a  grade  of  work. 


CHAPTER  XXXVII 

ECONOMICS  OF  BRIDGE  ENGINEERING   FIELDWORK 

The  economics  of  fieldwork  in  bridge  building  may  be  summed  up  in  the 
following  instructions  to  the  Resident  Engineer: 

First.  Start  work  ahead  of  the  contractor  so  as  to  have  all  the  triangu- 
lation  finished  and  bench-marks  estabhshed  before  he  is  ready  to  begin 
actual  operations. 

Second.  Employ  as  small  a  force  as  practicable  for  attending  properly 
to  all  work,  especially  the  inspection  of  materials  and  workmanship,  and 
retain  only  truly  competent,  energetic  men.  If  low-grade  helpers  are 
required  occasionally,  obtain  them  from  the  contractor,  and  be  sure  to  pay 
him  for  their  time,  unless  the  specifications  or  contract  provide  that  such 
labor  shall  be  furnished  free  of  charge,  as  is  often  the  case. 

Third.  See  that  the  entire  force  is  kept  really  busy  at  all  times.  This 
can  be  accomplished  by  laying  out  for  each  member  thereof  routine  work 
for  his  spare  moments. 

Fourth.  Before  any  construction  work  is  begun,  lay  out  on  paper  an 
economic  system  for  carrying  on  the  field  work  from  start  to  finish,  and  see 
thereafter  that  it  is  strictly  followed.  Should  at  any  time  any  develop- 
ment occur  that  would  render  advisable  a  modification  of  the  working 
schedule,  the  necessary  changes  therein  should  at  once  be  made;  and  all 
interested  parties  should  be  notified  in  writing  accordingly. 

Fifth.  Never  let  any  portion  of  the  work  drop  behind,  even  for  a  single 
day;  because  field  engineers  are  assumed  to  work  longer  hours  than  the 
staff  of  the  designing  office.  Field  engineers  should  live  on  the  job,  so  as 
to  be  ready  at  aU  hours  to  do  unexpected  work  and  to  meet  emergencies, 
consequently  they  have  no  cause  for  complaint  when  instructed  to  work 
overtime. 

Sixth.  See  that  the  home  office  is  supplied  strictly  on  time  with  the 
regular  field  reports,  and  send  in  special  ones  whenever  such  seem  necessary 
or  advisable. 

Seventh.  Do  the  testing  of  cement  far  enough  in  advance  of  its  use  to 
make  sure  of  its  having  the  requisite  strength;  and  if  therc^  be  any  other 
materials  to  be  inspected,  keep  the  work  of  inspection  well  in  advance  of 
the  demand. 

Eighth.  As  soon  as  materials  are  received  at  the  site,  see  that  they  are 
che(;ked  by  the  contractor  at  once,  and  report  immediately  to  tlie  home 
office  any  shortage  discovcncnl,  in  oider  that  it  may  be  made  good  before  it 
can  cause  delay  in  the  construction.     See  also  that  all  material  is  unloaded 

380 


ECONOMICS   OF   BRIDGE-ENGINEERING    FIELDWORK  381 

quickly,  even  if  the  onus  of  paying  for  demurrage  be  upon  the  contractor, 
because  it  is  economic  to  keep  the  railroad  officials  in  good  humor  by  return- 
ing their  cars  quickly,  and  because  it  does  not  take  many  unloaded  cars  to 
clutter  up  the  small,  temporary  yards  built  specially  for  the  job. 

Ninth.  Give  the  contractor  and  his  employees  every  aid  that  you  can 
legitimately,  short  of  assuming  duties  that  are  not  your  own — such  as  prep- 
aration of  bills  of  materials,  designs  for  plant,  etc.  By  keeping  the  force 
in  a  good  humor  the  work  will  be  expedited,  and  economy  for  all  concerned 
wiU  result. 

Tenth.  Make  all  monthly  estimates  promptly,  starting  in  two  or  three 
days  before  the  end  of  the  month,  if  that  be  necessary  to  accomplish  the 
purpose. 

Eleventh.  For  all  unclassified  work  or  so-called  ''extras,"  be  sure  to 
give  the  contractor  in  advance  written  instructions  to  do  the  same,  and  keep 
on  file  copies  of  ail  letters  containing  such  directions. 

Twelfth.  Keep  your  progress  reports  and  charts  up  to  date  so  that  you 
may  know  at  a  glance  what  proportion  of  each  class  of  work  on  the  job  is 
finished  and  what  proportion  remains  to  be  done. 

Thirteenth.  Remember  at  all  times  that  the  Resident  Engineer  is  a 
confidential  agent  and  not  a  principal,  and  be  governed  accordingly. 
While  he  has  the  right  to  discharge  at  any  time  any  of  his  employees  for 
just  cause,  he  should  keep  the  home  office  au  courant  with  the  character  of 
the  work  of  his  assistants,  in  order  that,  if  changes  in  the  staff  are  to  be 
made,  the  field  work  will  not  be  disorganized  thereby. 

Fourteenth.  If  practicable,  the  field  property  of  the  Engineers,  such  as 
instruments,  tapes,  testing  apparatus,  etc.,  should  be  insured  against  loss  • 
by  fire,  theft,  or  the  action  of  the  elements.  Sometimes  this  is  impossible; 
but  whether  it  is  or  not,  every  precaution  should  be  taken  to  prevent  such 
occurrences,  not  merely  because  of  the  pecuniary  loss  to  the  principals  but 
also  because  of  the  delay  to  the  fieldwork  that  would  be  likely  to  result. 

Fifteenth.  Copy  all  important  surveys  from  the  field  books  into  a 
survey-record  as  soon  as  made;  and  never  let  that  record  be  taken  into  the 
field,  for  its  loss  might  cause  great  inconvenience  and  expense.  When  loose- 
leaf  books  are  used  for  records  that  might  be  called  into  a  court  of  law, 
each  page  must  be  signed  and  dated  by  the  writer  thereof  at  the  time  he 
makes  the  record;  and  each  such  page  must  have  a  heading  or  title  which 
will  show  beyond  any  doubt  just  what  is  recorded  thereon  and  the  source 
of  the  information. 

Sixteenth.  Log  books  or  diaries  must  be  written  up  each  day,  whether 
there  was  any  work  done  or  not. 

Seventeenth.  As  a  great  many  of  the  Resident  Engineer's  duties  are  of 
a  semi-judicial  character,  all  of  his  acts  may  at  any  time  come  under  the 
review  or  inspection  of  a  court  of  law ;  hence  he  must  always  keep  this  in 
mind  when  making  decisions  or  compiling  records.  The  latter  must  be 
full,  concise,  and  so  made  as  to  be  admissible  as  evidence  in  a  suit  at  law. 


382  ECONOMICS   OF  BRIDGEWORK  Chaptee  XXXVII 

Eighteenth.  All  instruments  for  surveying  or  for  testing  materials, 
when  not  in  use,  must  be  kept  in  their  cases  or  boxes  in  the  Resident  Engi- 
neer's office.  No  transits  or  levels  should  be  left  set  up  around  derricks  or 
machinery  where  there  is  danger  of  their  being  struck  by  the  said  machinery 
or  by  teams,  unless  someone  is  left  to  guard  them. 

Nineteenth.  The  Resident  Engineer  must  be  careful  not  to  abuse  in 
any  way  the  rather  arbitrary  power  that  is  placed  in  his  hands;  but,  on 
the  other  hand,  he  must  not  fail  to  act  promptly  in  exercising  the  authority 
conferred  on  him,  if  it  be  necessary  to  do  so  in  order  to  protect  the  interests 
of  his  client  or  those  of  his  superiors. 

Twentieth.  See  that  all  materials  are  properly  stored  and  kept  in  good 
condition  until  used  in  the  construction;  and  make  sure  that  the  contractor 
takes  every  precaution  to  prevent  injury  to  them  from  fire  or  flood,  no 
matter  whose  property  they  may  be.  If  practicable,  they  should  be 
insured. 

Twenty-first.  Make  sure  that  no  damage  is  done  to  structural  steel  or 
reinforcing  bars  through  carelessness  in  handling  or  unloading. 

Twenty-second.  See  that  all  wooden  paving-blocks  are  ricked  up  in 
compact  piles  and  covered  so  as  to  prevent  checking;  and,  as  all  creosoted 
timber  is  very  inflammable,  take  every  precaution  against  its  being  injured 
by  fire. 

Twenty-third.  Make  sure  that  all  cement  is  properly  protected  against 
the  weather;  and  that  no  injured  cement  is  allowed  to  remain  on  the  job. 

Twenty-fourth.  Take  great  care  to  avoid  accident  in  the  storage  or  use 
of  explosives;  and  see  that  the  proper  charges  are  used. 

Twenty-fifth.  Make  sure  that  all  falsework  and  forms — in  respect  to 
both  design  and  quality  of  materials — are  fit  for  the  purpose  to  be  served; 
and  take  the  necessary  steps  to  prevent  unsightly  bulges  and  offsets  in 
concrete  surfaces  due  to  the  yielding  of  forms. 

Twenty-sixth.  In  sinking  cribs  or  caissons  do  not  permit  the  contractor 
to  allow  them  to  get  materially  out  of  position  or  tipped;  but  check  con- 
stantly for  line,  elevation,  and  verticality  until  all  danger  of  the  occurrence 
of  such  errors  of  any  magnitude  is  past. 

Twenty-seventh.  Look  carefully  to  the  building  up  of  cribs  and  caissons; 
because,  if  they  become  badly  warped  or  twisted,  much  needless  expense 
and  delay  will  be  involved. 

Twenty-eighth.  Watch  carefully  the  depositing  under  water  of  all  con- 
crete so  as  to  make  sure  that  it  is  not  injured  in  the  process  of  placing. 

The  preceding  instructions,  of  course,  could  readily  be  extended  by 
entering  more  into  detail,  and  it  is  true  that  the  Resident  Engineer  should 
study  and  follow  closely  many  other  directions,  both  written  and  oral,  given 
him  by  his  superiors;  but  enough  has  already  been  said  in  this  chapter  to 
indicate  the  necessity  for  a  proper  application  to  fieldwork  of  the  principles 
of  economics,  what  the  said  principles  are,  and  how  they  should  be  utilized. 


CHAPTER  XXXVIII 

ECONOMICS   OF   BRIDGE-CONTRACTOr's   GENERAL   FIELDWORK 

The  data  for  this  chapter  were  furnished  by  Mr.  H.  K.  Seltzer,  C.E.,  of 
the  Union  Bridge  and  Construction  Company,  and,  in  years  long  gone  by, 
one  of  the  author's  principal  assistant  engineers.  As  that  Company  is  one 
of  the  most  experienced  and  successful  bridge-contracting  firms  in  America, 
what  Mr.  Seltzer  has  to  say  about  the  economics  of  his  specialty  ought  to  be 
authoritative. 

The  Contractor  who  has  been  awarded  a  contract  naturally  says  to  him- 
self— "I  must  do  this  work  as  quickly  and  as  economically  as  practicable." 
He,  therefore,  gives  thorough  consideration  to  the  problem  of  how  this 
result  can  be  brought  about;  and,  while  so  doing,  he  should  think  not  only 
of  the  profit  he  expects  to  make,  but  also  of  the  fact  that  he  must  maintain 
his  good  reputation,  and  improve  it,  if  possible.  In  order  to  complete  the 
work  promptly  and  economically,  he  should  devote  careful  thought  to  the 
following  subjects: 

1.  The  Field  Organization. 

2.  Plant. 

3.  Yards,  Wharves,  and  Tracks. 

4.  Plans  of  Buildings  and  Plant. 

5.  Materials  and  Supplies. 

6.  General. 

1.    The  Field  Organization 

The  man  in  active  charge  should  have  had  previous  experience,  either  as  a 
superintendent  or  engineer  of  construction,  in  charge  of  similar  work.  It  is 
not  absolutely  necessary  that  he  should  have  managed  work  equally 
large  or  important;  but  he  should  certainly  be  a  man  of  character  and 
force.  He  may  be  known  as  Chief  Engineer,  Manager,  General  Superin- 
tendent, or  Engineer  of  Construction.  We  shall  assume  that  he  is  an 
engineer  and  that  his  company  has  designated  him  as  "Engineer  of  Con- 
struction." He  should  have  the  following  general  assistants,  if  the  size  of 
the  work  warrant  it, — these  men  to  report  to  him  directly: 

Assistant  Engineer  of  Construction.  General  assistant  to  Engineer  of 
Construction.     In  charge  of  field  and  office  engineering  work. 

Superintendent.  In  charge  of  all  foremen,  including  the  master  me- 
chanic. The  superintendent  should  have  complete  charge  of  work  in  field 
and  should  be  a  capable  and  reliable  man. 

383 


384  ECONOMICS   OF   BRIDGEWORK         Chapter  XXXVIII 

Purchasing  Agent.  The  making  of  all  purchases  should  be  placed 
in  the  hands  of  a  competent  man.  Schedules  of  materials  and  supplies 
should  be  furnished  to  him  by  the  office  engineers,  specifying  when  they 
will  be  required;  and  he  should  arrange  his  deUveries  as  nearly  as  possible 
in  that  order. 

Accountant  or  Auditor.  In  charge  of  all  office  work  outside  of  the 
engineering  department.  He  should  have  charge  of  bookkeepers,  pay- 
masters, timekeepers,  cost  accountants,  material  checkers,  storehouse  men, 
and  any  other  clerical  help  required. 

2.  Plant. 

The  best  plant  obtainable  should  be  provided  in  sufficient  qaantity  to 
permit  of  the  rapid  execution  of  the  work  with  the  smallest  possible  number 
of  men.  Hand,  air,  or  electrical  tools  should  be  liberally  provided.  There 
should  also  be  furnished  spare  equipment,  such  as  an  extra  hoisting  engine, 
an  extra  derrick,  and  an  extra  dredge-bucket.  On  large  jobs  of  work  these 
extra  pieces  of  equipment  are  always  needed  because  of  breakdowns.  A 
liberal  supply  of  repair  parts  for  engines,  pumps,  pneumatic  tools,  etc., 
should  always  be  kept  on  hand. 

3.  Yards,  Wharves,  and  Tracks. 

Sufficient  ground  should  be  obtained  to  provide  storage  room  and  space 
for  the  necessary  operations.  Existing  wharves  should  be  secured,  when 
they  can  be  had,  and  new  ones  built  when  necessary.  A  plan  should  be 
prepared  showing  the  exact  location  of  railroad  tracks,  storage  grounds, 
buildings,  and  wharves.  The  arrangement,  of  course,  will  depend  to  a  great 
degree  on  the  ground  and  the  river  front  available;  and  the  cost  and 
progress  of  the  work  will  vary  largely  with  the  care  and  attention  given  to 
this  subject. 

4.  Plans  of  Buildings  and  Plant. 

After  it  is  known  just  what  yard-room  can  be  secured,  and  after  a 
general  ground-layout  has  been  drafted,  detailed  plans  of  buildings,  der- 
ricks, and  other  material-handling  devices  should  be  prepared;  then  the 
necessary  bills  of  material  should  be  made  therefrom.  These  plans  should 
include  drawings  of  barges,  pile-drivers,  falsework,  etc. — in  fact  of  every- 
thing that  must  be  built  at  the  bridge  site. 

While  planning  buildings  and  barges,  it  is  well  to  give  consideration  to 
the  fact  that,  after  the  completion  of  the  job,  buyers  may  be  obtained  in  the 
vicinity,  provided  such  constructions  are  so  designed  as  to  meet  local  con- 
ditions and  requirements. 

5.  Materials  and  Supplies. 

Schedules  of  materials  for  both  construction  and  permanent  work 
should  be  made  as  quickly  as  possible,  even  though  the  contractor  may 
have  contracted  for  his  materials  bofoic  bidcUng.  It  is  important  that  no 
time  be  lost,  in  order  that  early  shipments  may  be  made;    and,  again, 


BRIDGE-CONTRACTORS     GENERAL     FIELDWORK  385 

prices  change  so  rapidly  that  those  used  in  bidding  may  not  hold  in  every 
case,  especially  if  there  be  considerable  delay. 

Materials  should  be  ordered  for  shipment  as  nearly  as  possible  in  the 
order  required.  It  frequently  occurs  that  no  special  attention  is  given  to 
this  point;  and,  as  a  result,  delay  and  unnecessary  cost  are  involved. 

Contracts  for  fuel,  oil,  water,  electricity,  and  supplies  should  be  made 
immediately,  whenever  it  appears  to  the  contractor's  advantage  so  to  do. 

6.     General 

It  pays  well  to  have  satisfied  and  loyal  employees;  and  every  effort 
should  be  made  to  provide  and  maintain  such  a  force.  Special  care  should 
be  used  in  the  selection  of  the  skeleton  organization,  including  the  foreman; 
and  these  men  and  all  other  employees  should  be  well  paid,  and  given  the 
best  treatment  possible.  Where  camps  are  necessary,  they  should  be  sani- 
tary; and  good  food  should  be  provided  at  actual  cost. 

It  is  well  to  prepare  in  advance  a  schedule  of  the  progress  of  the  work 
that  it  is  intended  to  follow;  and  plans  should  be  made  accordingly  so  as  to 
carry  it  out. 

Daily  unit  costs  should  be  kept,  when  possible,  in  addition  to  the  usual 
cost  system;  and  the  foremen  and  all  others  interested  should  be  advised 
how  well  they  are  found  to  be  doing,  comparisons  being  drawn  with  other 
work  of  a  similar  nature. 

Nothing  should  be  done  by  hand  that  can  be  accomplished  with  ma- 
chinery or  power  tools. 

In  concluding  this  chapter,  the  author  begs  to  make,  for  the  benefit  of 
progressive  contractors,  the  following  additional  suggestion,  based  upon 
extended  experience  and  close  observation  of  bridge  builders  and  their 
methods  of  operation: 

It  is  almost  always  consistent  with  true  economy  to  push  every  piece  of 
work  to  completion  as  rapidly  as  practicable,  even  if  by  so  doing  there 
should  be  involved  additional  expense  (of  course  within  the  bounds  of 
reason)  for  outfit  and  labor;  because  the  time  thus  saved  can  generally  be 
more  advantageously  devoted  to  another  Job. 


CHAPTER  XXXIX 

ECONOMICS    OF   CONCEETE   MIXING 

In  the  mixing  of  concrete  there  arise  many  economic  problems,  most  of 
which  are  apparently  of  such  minor  importance  as  not  to  be  worthy  of 
consideration.  For  small  jobs  of  work  this  may  be  true  enough,  but  on 
large  ones,  involving  great  yardage  of  concrete,  every  httle  item  of  economy 
is  well  worth  while. 

There  are  two  main  points  of  view  from  which  this  question  may 
be  considered — that  of  the  contractor  and  that  of  the  engineer — the  latter, 
of  course,  acting  for  the  best  interests  of  his  client.  The  contractor  gen- 
erally is  paid  for  concrete  in  place  at  so  much  per  cubic  yard;  but  there  are 
often  several  unit  prices  arranged  to  cover  varying  conditions.  Sometimes 
these  conditions  are  variations  in  the  composition  of  the  mixture,  but  often 
they  relate  to  the  differing  costs  of  placing  and  form  work.  Be  this  as  it 
may,  though,  in  ordinary  specifications  there  is  nothing  to  induce  the  con- 
tractor to  try  to  produce  the  strongest  and  best  concrete  practicable.  This 
is  the  duty  of  the  engineer;  and  he  accomplishes  it  by  stating  clearly  in  his 
specifications  the  qualities  of  all  the  materials  employed,  the  compositions 
of  the  different  classes  of  concrete,  how  the  components  thereof  are  to  be 
mixed,  how  the  fresh  concrete  is  to  be  placed,  and  how  the  finished  work  is 
to  be  protected  until  the  mass  hardens  and  dries — also  by  carefully 
inspecting  the  materials  for  quality,  the  mixing,  the  placing,  and  the 
protection,  so  as  to  ensure  that  the  specifications  are  fully  comphed  with. 

Ordinarily  there  are  not  many  legitunate  major  ways  in  which  the 
contractor  may  economize  in  his  concrete-work,  as  he  is  confined  mainly  to 
purchasing  the  materials  as  cheaply  as  possible,  doing  the  mixing  economic- 
ally, and  placing  the  mixture  expeditiously ;  but  occasionally  he  is  given  an 
opportunity  to  economize  on  the  quantity  of  cement  by  the  engineer's 
having  made  it  proportional  to  the  volume  of  voids  in  the  aggregate,  and 
by  being  permitted  to  use  one-man  stones  in  the  mass. 

There  are,  however,  many  minor  ways  in  which  the  contractor  may 
legitimately  economize  in  the  making  of  concrete,  principally  by  the  appli- 
cation of  forethought  in  the  receiving  and  storing  of  materials  promptly; 
locating  the  bins  in  the  most  favorable  places  for  expediting  the  work; 
csta))lishing  the  best  practicable  scheme  for  transportation  from  bins  to 
mixers  and  from  mixers  to  points  of  deposit;  substituting  machinery  for 
man-power  wherever  it  will  facilitate  the  work  and  reduce  cost;  designing 
and  building  forms  that  are  not  too  expensive,  that  can  be  placed  and 
removed  expeditiously,  and  that  have  some  salvage  value;  and  installing 

3SG 


ECONOMICS  OF  CONCRETE   MIXING 


387 


efficient  and  not-too-expensive  apparatus  for  protecting  the  finished  con- 
crete from  injury  by  frost  or  heat.  Doing  all  these  things  scientifically  and 
systematically  will  often  enable  a  contractor  to  make  money  out  of  a  job  on 
which  otherwise  there  would  have  been  a  loss. 

Amongst  the  economic  problems  that  arise  in  the  manufacture  of  con- 
crete, the  principal  ones  are  the  following: 

A.  Best  proportions  of  materials. 

B.  Reduction  of  voids  in  the  aggregate. 

C.  Using  a  mixture  of  gravel  and  sand  without  screening.  > 

D.  Waterproofing. 

E.  Increasing  fluidity  of  mixture. 

F.  Manner  and  time  of  mixing. 

G.  Amount  of  mixing  water. 
H.    Use  of  large  stones  in  mass. 

I.      Vibration  and  jigging  of  newly  placed  concrete. 
J.     Age  of  cement. 
K.    Protection  of  fresh  concrete. 

Each  of  these  economic  questions  will  be  taken  up  in  the  above  order 
and  discussed  in  detail. 


Best  Proportions  of  Materials 

Without  knowing  in  advance  the  kinds  and  characteristics  of  the  aggre- 
gates which  the  successful  bidder  will  employ,  it  is  impracticable  for  an 
engineer  to  specify  the  best  possible  proportions  for  concrete,  hence  he  is. 
either  compelled  to  name  three  or  four  standard  mixtures  or  else  to  specify 
certain  maximum  limits  of  the  materials  in  the  aggregate  and  an  amount 
of  cement  proportionate  to  the  volume  of  voids  therein. 

The  principle  to  be  adopted  in  specifying  the  proportions  for  concrete  is 
to  use  a  little  more  than  enough  cement  to  fill  the  voids  in  the  sand  and  a 
little  more  than  enough  of  the  resulting  mortar  to  fill  the  voids  in  the 
broken  stone  or  gravel.  If  the  mixing  were  perfect,  there  might  not  be 
good  reason  for  these  excesses  of  cement  and  mortar;  but,  of  course,  it 
never  is.  The  author  is  satisfied  with  an  excess  of  ten  per  cent  for  each 
case,  or  with  an  excess  of  ten  per  cent  of  cement  above  the  volume  of  voids 
in  the  aggregate. 

The  most  common  proportions  specified  are  those  given  in  the  following 

table: 

TABLE   39a 


Ingredients 

Proportions 

Cement    

1 

2 
3 

1 

2 
4 

1 

21 
5 

1 
3 
5 

1 
3 
6 

Sand.        

Broken  stone  or  gravel.  .  . 

388  ECONOMICS   OF   BRIDGEWORK  Chapter  XXXIX 

The  mixture  of  1  :  3  :  5  used  to  be  the  standard  for  concrete  in  large 
masses  placed  in  the  dry,  but  there  are  certain  sands  of  such  uniform  grain- 
size  that  one  portion  of  cement  to  three  of  sand  will  not  fill  all  the  voids 
therein;  and,  although  the  mortar  produced  will  be  ample  in  amount  to 
fill  all  the  voids  in  the  stone  or  gravel,  the  mass  resulting  will  be  permeable 
by  water,  and,  therefore,  not  first-class  concrete. 

The  proportion  of  1  :  2|  :  5  is  better  than  that  of  1:3:5,  because 
the  amount  of  cement  is  always  more  than  enough  to  fill  the  voids  in  the 
sand,  and  that  of  the  mortar  is  more  than  enough  to  fill  the  voids  in  the 
stone  or  gravel.  It  is  a  perfectly  safe  mixture  but  not  an  economic  one. 
It  is  being  rather  widely  specified  today  for  mass  concrete  placed  in  the 
dry;  and  for  small  jobs  it  is  a  good  one  to  adopt  therefor. 

The  proportion  of  1  :  2  :  4  is  the  common  one  for  reinforced-concrete; 
and  the  stone  or  gravel  should  not  be  very  coarse,  because  otherwise  the 
concrete  would  not  flow  properly  between  the  reinforcing  bars,  and  voids 
might  result.  In  view  of  the  importance  of  having  reinforced-concrete 
as  perfect  as  possible,  and  of  the  fact  that  the  mortar  should  take  a  firm 
grip  on  the  reinforcing  bars,  it  is  not  advisable  to  use  for  this  purpose  any 
concrete  less  rich  in  cement  than  this  mixture. 

The  proportion  of  1:2:3  with  fine  broken  stone  or  gravel  is  the 
author's  standard  for  concrete  to  be  deposited  through  water  by  tremie  or 
trip-bucket.  It  contains  an  excess  of  cement  to  provide  for  the  contin- 
gency that,  in  spite  of  all  precautions,  there  may  be  a  slight  flow  of  water 
through  some  portion  of  the  concrete.  The  author  has  often  had  occasion 
to  examine  concrete  of  this  mixture  placed  through  water,  and  has  invariably 
found  it  to  be  perfectly  satisfactory,  in  fact,  just  as  good  as  the  less-rich 
concrete  placed  in  the  dry.  It  has  been  stated  by  good  authority  that  this 
proportion  makes  much  better  concrete  for  reinforced  work  than  does  the 
standard  proportion  of  1  :  2  :  4;  hence  it  might  prove  economic  to  adopt 
the  richer  mixture  therefor,  but  it  would  first  be  necessary  to  educate  the 
profession  to  the  advisability  of  the  innovation. 

The  only  excuse  for  adopting  in  a  specification  a  general  clause  for  a 
1:3:6  mixture  is  to  save  expense  in  a  structure  where  the  total  cost  has 
to  be  hold  down  to  an  absolute  minimum,  in  order  to  meet  a  limited  appro- 
priation ;  and  then  it  should  usually  be  confined  to  locations  below  ground 
where  no  frost  can  reach.  It  would  be  legitimate  to  adopt  it  for  large 
anchorages  where  great  mass  is  required,  in  which  case  it  might  have  to  be 
faced  with  richer  concrete  and  employed  only  in  locahties  where  the  climate 
is  mild.  But  when  special  care  is  taken  in  the  grading  of  the  aggregate,  a 
1:3:0  proportion  can  safely  1)0  employed,  because  in  gradini  santl  the  1  to 
3  proportion  will  fill  all  voids  in  the  mortar,  and  the  latter  will  fill  all  voids 
in  the  stone,  thus  producing  satisfactory  concrete,  providing,  of  course, 
that  the  mixing  be  thoroughly  done. 

The  1:3:6  mixture  does  not  always  make  good  concrete,  and  the 
author  would  hesitate  a  long  time  before  deciding  to  adopt  it  on  any  of 


ECONOMICS   OF   CONCRETE   MIXING 


389 


his  constructions.  He  did  once  use  it  for  some  below-ground  work  on  a 
bridge  in  Southern  CaHfornia,  in  which  every  legitimate  effort  had  to  be 
made  to  keep  the  total  cost  of  structure  within  a  limit  of  $200,000.  There 
proved  to  be  a  margin  of  less  than  $500  when  the  bridge  was  finally  com- 
pleted and  turned  over  to  the  owners. 

Concretes  as  poor  as  1  :  4  :  8  or  even  1  :  6  :  10  have  been  used  in  times 
past  in  large  mass-work,  in  order  to  reduce  the  cost  of  construction;  but, 
in  the  author's  opinion,  such  mixtures  are  not  legitimate.  Some  tests  on 
plain  concrete  beams  by  Wm.  B.  Fuller,  Esq.,  gave  on  the  average  the 
moduli  of  rupture  indicated  in  the  following  table: 

TABLE   396 


Proportions  by 

Proportions  by 

Modulus  of 

Weights  of  Cement, 

Volume  of  Cement, 

Rupture.     (Lbs. 

Sand,  and  Stone 

Sand,  and  Stone 

per  Sq.  In.)  Average 

1:2:4 

1  :  2.34  :    4.12 

439 

2 

5 

2.34 

5.17 

380 

3 

5 

3.51 

5.17 

285 

3 

6 

3.51 

6.21 

226 

4 

8 

4.68 

8.25 

157 

6 

10 

7.02 

10.34 

89 

This  table  gives  a  very  clear  idea  of  the  relative  strengths  of  concrete  of 
varying  richnesses;  and  it  is  evident  therefrom  that  the  last  two  mixtures 
are  too  poor  to  warrant  use  in  any  first-class  construction,  also  that 
1  :  2|  :  5  concrete  is  better  than  1  :  3|  :  5  concrete  in  the  ratio  of  1.33.  By 
interpolation  it  may  be  concluded  that  it  is  probably  better  than  1:3:5 
concrete  in  the  ratio  of  about  1.2.  Comparing  the  1  :  2|  :  5  mixture  with 
the  1:3:6  one,  the  ratio  of  strengths  would  be  about  1.5. 


Reduction  of  Voids  in  the  Aggregate 

Whenevesr  there  is  a  large  amount  of  concreting  to  be  done  on  a  job,  it 
will  prove  to  be  economical  to  study  carefully  the  percentage  of  voids  in  the 
aggregate  of  broken  stone  and  sand  (or  of  gravel  and  sand),  and  to  experi- 
ment in  order  to  determine  what  mixture  of  broken  stone  and  gravel,  or  of 
several  sizes  of  broken  stone,  with  the  proper  amount  of  sand  in  each  case, 
will  reduce  the  said  percentage  of  voids  to  a  minimum.  If  then  this  mixed 
aggregate  be  adopted,  and  if  the  amount  of  cement  is  never  less  than  one 
and  a  tenth  times  the  volume  of  voids,  the  resulting  product  will  be  first- 
class  and  satisfactory  to  all  concerned,  provided,  of  course,  that  only 
proper  materials  be  employed  and  that  the  mixing  be  thorough. 

As  a  matter  of  precaution,  however,  against  carelessness  or  error  on  the 
part  of  the  tester  of  voids,  the  author's  specifications  require  that,  for  aggre- 
gates in  which  all  the  materials  are  measured  separately  before  mixing, 


390  ECONOMICS   OF  BEIDGEWORK  Chapter  XXXIX 

there  shall  be  used  not  less  than  420  lbs.  of  cement  per  cubic  yard  of  finished 
concrete,  excluding,  of  course,  the  space  occupied  by  any  one-man  stones 
that  it  may  contain. 

Using  a  Mixture  of  Gravel  and  Sand  without  Screening. 

If  there  be  available  and  located  convenient!}^  for  the  work  a  large  body 
of  clean,  mixed  gravel  and  sand,  it  may  prove  economical  to  use  it  without 
screening  in  one  of  two  ways,  viz. : 

First.  By  constantly  making  tests  and  finding  what  amount  of  sand  or 
of  gravel  should  be  added  to  the  natural  mixture  in  order  to  secure  the 
correct  proportions,  sifting  out  a  supply  of  the  material  required,  stoi'ing  it 
close  at  hand  for  use,  and  combining  it  with  the  said  natural  mixture ;  and 

Second.     By  using  the  natural  mixture  directly  as  it  comes  from  the  pit. 

In  either  case  the  rule  previously  given  for  a  volume  of  cement  equal  to 
at  least  one  and  one-tenth  times  that  of  the  voids  should  be  followed;  and 
as  a  matter  of  precaution,  the  amount  per  cubic  yard  of  finished  concrete 
(excluding  all  embedded  one-man  stones)  should  be  460  lbs.  for  the  first- 
mentioned  of  these  two  methods  and  500  lbs.  for  the  second.  This  is  in 
accordance  with  the  author's  standard  specifications. 

Whether  it  is  most  economic  to  separate  all  the  ingredients  of  the  natural 
mixture  and  re-mix  in  the  desired  proportions,  to  add  sand  or  gravel  to 
the  natural  mixture,  or  to  use  the  pit  run,  can-only  be  determined  for  each 
case  as  it  arises  by  some  very  careful  computing,  based  upon  the  governing 
prices  of  labor  and  materials.  In  fact  it  might  be  necessary  to  make  some 
actual  experiments.  If  labor  were  very  high  and  the  price  of  cement 
dehvered  at  site  were  reasonably  low,  it  would  probably  be  most  economical 
to  use  80  lbs.  extra  of  cement  per  cubic  yard  of  concrete  and  employ  the 
pit  run;  but  if  cement  were  very  expensive  and  labor  cheap,  it  would  be 
most  economical  to  sift  the  natural  mixture  and  remix. 

Whether  adding  either  sand  or  gravel  to  the  natural  mixture,  in  order  to 
bring  it  to  best  proportions  is  economical,  will  depend  upon  whether  the 
screening  out  and  incorporating  of  the  additional  material  and  the  occa- 
sional testing  of  the  pit  run  will  cost  less  than  the  40  lbs.  of  cement  saved 
per  cubic  yard  of  finished  concrete. 

Waterproofing 

In  certain  places  it  is  necessary  that  the  construction  should  be  abso- 
lutely waterproof;  and  whether  accomplishing  this  is  to  be  done  by  adding 
some  foreign  ingredient  to  the  cement  or  by  inserting  a  layer  of  burlaj:)  or 
other  similar  material  covered  with  pitch  or  asphaltum  applied  hot  is  a 
pi()})l('ni  in  economics  that  has  to  be  solved  for  each  case  by  some  close 
figuring.  There  are  on  the  market  several  patented  materials  to  add  to 
concrete  for  waterproofing,  the  manufacturer  of  each  of  which  claims  it  to 
be  the  best  possible  for  the  purpose;  but,  as  far  as  the  author  knows,  there 


ECONOMICS  or  CONCRETE  MIXING  391 

is  nothing  better  than  the  addition  of  hydrated  lime  to  the  cement  to  the 
amount  of  about  ten  per  cent  of  its  volume.  In  any  case  where  the  condi- 
tion of  impermeability  is  paramount,  it  would  be  well  to  adopt  both  of  these 
expedients,  irrespective  of  cost;  and  the  combined  expedients,  if  success- 
ful, would  effect  a  true  economy.  The  question  of  the  economics  of  water- 
proofing concrete  is  treated  at  length  in  Chapter  XLIII. 

Increasing  Fluidity  of  Mixture 

The  addition  to  the  cement  of  not  more  than  ten  per  cent  of  its  volume 
of  hydrated  lime  not  only  tends  to  make  the  finished  work  waterproof,  but 
also  adds  greatly  to  the  fluidity  of  the  mixture,  thus  facihtating  the  placing 
of  it  around  the  reinforcing  bars.  Certain  reliable  tests  have  shown  that 
the  addition  of  lime  up  to  fifteen  per  cent  of  the  volume  of  cement  really 
slightly  increases  the  tensile  strength  after  some  three  weeks;  and  as  the 
addition  of  lime  does  not  add  materially  to  the  expense  of  the  concrete,  it  is 
a  matter  of  true  economy  to  employ  it.  The  beneficial  effect  of  hydrated 
lime  is  partly  due  to  the  fact  that  it  permits  a  reduction  in  the  amount  of 
mixing  water  without  lessening  the  plasticity  of  the  mixture. 

Manner  and  Time  of  Mixing 

Almost  all  concrete  nowadays  is  mixed  by  machinery,  and  preferably 
in  batch  mixers,  although  .some  continuous  mixers  have  been  known  to 
give  good  results.  The  strength  of  the  concrete  is  augmented  as  the  time 
of  mixing  is  increased;  hence  it  is  an  economic  problem  for  the  engineer, 
hut  not  for  the  contractor,  to  determine  what  is  the  best  time  to  adopt  for 
mixing  each  batch.  If  the  time  be  made  too  short,  the  attainable  strength 
and  quality  of  the  concrete  are  not  developed;  while  if  it  be  made  too  long, 
the  output  per  mixer  is  reduced  and  the  cost  per  cubic  yard  of  the  finished 
work  is  increased.  As  the  contractor  is  paid  so  much  per  cubic  yard  for 
concrete  in  place,  it  is  evident  that  he  always  loses  instead  of  gains  by 
increasing  the  time  of  mixing,  and  that  the  owner,  up  to  a  certain  point,  is  a 
gainer  by  such  an  increase,  after  which  he  is  a  loser.  In  respect  to  what 
that  Umit  is,  most  engineers  differ.  Contractors  would  like  to  make  it 
thirty  seconds,  but  are  willing  to  concede  a  fuU  minute.  The  author,  how- 
ever, would  set  a  minimum  of  two  minutes.  As  loading  and  unloading  the 
mixer  require  for  the  two  operations,  on  an  average,  about  45  seconds,  and 
as  the  time  given  to  actual  mixing  is  about  the  same,  the  total  time  needed 
per  batch  is  one  and  a  half  minutes,  but  when  the  time  of  rotating  the  mixer 
is  increased  to  two  minutes,  the  total  time  per  batch  is  two  minutes  and 
forty-five  seconds,  hence  the  output  per  mixer  would  be  nearly  halved. 
Nevertheless,  the  author  beheves  that  doubhng  the  ordinary  time  of 
mixing  will  result  in  true  economy  for  the  owner.  The  authorities  recog- 
nize that  it  is  far  better,  when  a  truly-first-class  job  is  required,  to  employ 
more  mkers,  even  at  a  higher  first-cost  for  equipment,  and  work  them  on  a 


392  ECONOMICS   OF  BRIDGE  WORK  Chapter  XXXIX 

longer  schedule,  than  it  is  to  try  with  each  single  mixer  to  produce  the 
greatest  possible  yardage  in  the  least  practicable  time. 

Greater  care  and  increased  expense  in  mixing  and  placing  are  in  the  hne 
of  true  economy;  for  they  produce  a  stronger  concrete  and,  therefore, 
justify  the  use  of  higher  unit  stresses  and  a  consequent  reduction  in  the 
concrete  sections.  This  question  is  of  especial  importance  for  concrete  slabs 
on  long-span  steel-bridges,  and  in  long-span  concrete-bridges. 

Amount  of  Mixing  Water 

It  has  been  the  general  practice  to  use  very  wet  mixes,  especially  for 
reinforced-concrete.  From  the  construction  standpoint  this  is  economical, 
as  it  reduces  considerably  the  cost  of  handling  and  placing.  Recent  investi- 
gation, however,  has  shown  that  an  excess  of  water  reduces  the  strength  of 
the  concrete  very  materially,  and  makes  the  concrete  porous;  it  also  tends 
to  cause  segregation  of  the  materials.  The  use  of  an  excess  of  water  is, 
therefore,  false  economy.  The  new  American  Railway  Engineering  Asso- 
ciation Specification  for  Plain  and  Reinforced-Concrete  contains  the 
following  requirement: 

The  quantity  of  water  used  in  mLxing  shall  be  the  least  amount  that  will  produce 
a  plastic  or  workable  mixture  which  can  be  worked  into  the  forms  and  around  the  rein- 
forcement. Under  no  circumstances  shall  the  consistencj'^  of  the  concrete  be  such  as  to 
permit  a  separation  of  the  coarse  aggregate  from  the  mortar  in  handling.  An  excess  of 
water  will  not  be  permitted,  as  it  seriously  affects  the  strength  of  the  concrete;  and  any 
batch  containing  such  an  excess  will  be  rejected. 

Use  of  Large  Stones  in  the  Mass 

When  the  contractor  is  permitted,  under  certain  restrictions,  to  place 
one-man  stones  in  the  concrete  in  order  to  save  mortar,  he  usually  thinks  he 
has  a  "soft  snap,"  but  sometimes  this  is  not  the  case;  because,  in  addition 
to  their  having  to  be  carried  to  the  site,  they  must  be  thoroughly  cleaned  and 
wetted  before  being  placed.  This  placing  when  properly  performed  takes 
time,  and  is  done  by  man  power — not  by  machinery.  Again,  such  one- 
man  stones  are  generally  boulders  taken  from  the  river  bed,  where  they  are 
often  found  covered  with  moss  and  slime,  all  of  which  has  to  be  carefully 
removed.  In  the  old  days  when  labor  was  cheap  and  cement  expensive, 
these  one-man  stones  were  looked  upon  as  plums  in  the  pudding,  but  today 
the  same  volume  of  straight,  machine-made  concrete  will  often  prove  less 
costly  than  the  said  "plums."  In  case,  however,  there  is  old  stone  masonry 
to  disposer  of,  it  will  generally  be  found  cheaper  to  use  it  as  one-man  stone 
in  the  concrete  rather  than  to  haul  it  away. 

Vibration  and  Jigging  of  Freshly-made  Concrete 

During  the  past  year  there  has  been  considerable  talk  about  the  bene- 
fits to  be  derived  by  fresh  concrete  through  vibration  and  jigging;  but  the 


ECONOMICS   OF   CONCRETE   MIXING  393 

truth  is  that,  while  such  treatment  sometimes  augments  the  strength,  it 
often  has  the  opposite  effect.  From  the  resume  of  an  able  paper  by  Prof. 
Duff  A.  Abrams  entitled  '  'Effect  of  Vibration,  Jigging,  and  Pressure  on 
Fresh  Concrete"  the  author  extracts  the  following: 

The  indications  of  the  vibration  and  jigging  tests  should  not  be  misinterpreted. 
The  tests  show  that,  after  the  concrete  is  properhj  placed,  these  methods  of  treatment  do 
no  good,  and  may  be  harmful,  if  too  severe  or  too  long  continued.  However,  there 
can  be  no  doubt  of  the  value  of  such  methods  for  getting  concrete  into  place  in  intricate 
forms  and  around  reinforcing  bars.  The  tests  are  of  value  in  showing  that  this  is  the 
only  desirable  function  of  such  treatments. 

The  tests  show  that,  with  jigging,  high  strength  may  be  secured  with  drier  mixes 
.than  would  otherwise  be  feasible.  It  is  a  matter  of  common  experience  that  concrete 
of  drier  consistency  (and  consequently  higher  strength)  can  be  placed  by  means  of  jig- 
ging or  vibration  than  would  be  possible  by  the  usual  methods. 

It  is  clear  from  these  tests  that  if  tamping,  vibration,  or  pressure  on  fresh  concrete 
is  to  be  effective  in  increasing  its  strength  three  factors  must  be  kept  in  mind. 

(1)  We  must  take  advantage  of  the  fact  that  with  these  methods  the  concrete  can 
be  placed  and  finished  drier  than  with  ordinary  methods. 

(2)  Excess  water  which  is  brought  to  the  surface  must  be  removed. 

(3)  We  must  take  advantage  of  the  fact  that  aggregate  of  a  coarser  grading  may 
be  used  when  such  methods  are  employed  than  would  be  practicable  otherwise. 

The  advantages  to  be  gained  under  (3)  are  due  to  the  fact  that,  up  to  a  certain  point, 
a  plastic  mix  can  be  secured  with  a  smaller  quantity  of  water,  if  the  aggregate  is  as 
coarse  as  practicable.  Unless  these  precautions  are  taken,  tamping  and  vibration  are  of 
doubtful  value. 

Age  of  Cement 

Prof.  Abrams  ha,s  lately  proved  that  the  ultimate  strength  of  concrete 
in  compression  is  a  function  of  the  age  of  the  cement  at  time  of  mixing,  the 
fresher  it  is  the  greater  the  strength.  This  is  at  variance  with  the  idea 
which  governed  previously,  viz.,  that  cement  is  better  for  a  httle  aging; 
but  we  are  learning  these  days  that  many  of  our  old  ideas  about  cement  and 
concrete  were  incorrect. 

In  Bulletin  No.  6  of  the  Structural  Materials  Research  Laboratory  of 
Lewis  Institute,  Prof.  Abrams  presents  a  number  of  diagrams  showing  the 
percentages  of  loss  of  strength  in  compression  for  concrete  by  using  cement 
that  had  been  stored  from  two  to  twenty-four  months,  as  compared  with 
that  manufactured  with  perfectly  fresh  cement;  and  the  amounts  thereof 
are  surprising.  They  average  fifteen  per  cent  for  two  months  and  fifty-five 
per  cent  for  twenty-four  months,  with  almost  proportionate  percentages 
for  intermediate  periods.  However,  the  loss  is  not  quite  as  bad  as  these 
figures  would  show,  because  the  experiments  prove  that  the  concrete  tends 
to  recover  its  strength  with  age.  For  instance,  when  two-months-old 
cement  is  employed,  the  loss  is  nineteen  per  cent  at  one  month  and  only 
eleven  per  cent  at  two  years;  and  when  two-year-old  cement  is  used  the 
loss  is  fifty-six  per  cent  at  one  month  and  only  forty-two  per  cent  at  one 
year. 


394  ECONOMICS  OF  BRIDGEWOKK  Chapter  XXXIX 

The  large  amounts  of  these  losses  indicate  clearly  the  desirability  (from 
the  standpoint  of  the  strength  of  the  finished  product)  of  using  cement  as 
soon  after  grinding  as  is  practicable.  It  must  not  be  forgotten,  however, 
that  cement  which  has  had  no  aging  is  hkely  to  be  deficient  in  regard  to 
soundness;  so  that  its  testing  in  respect  to  this  requirement  should  be 
extremely  thorough.  The  author  for  many  years  has  insisted  upon  twenty- 
eight  day  tests  on  cement  whenever  that  arrangement  would  not  delay  the 
progress  of  the  work;  but  on  the  strength  of  Prof.  Abrams'  findings,  he 
would  now  be  willing  to  accept  on  seven-day  tests  any  standard  cement 
with  which  he  is  acquainted. 

Again,  the  author  has  sometimes  made  arrangements  for  testing  and 
storing  large  quantities  of  cement  at  the  manufactory,  so  as  to  have  it 
available  when  needed ;  but  he  may  now  be  obliged  to  forego  this  practice. 

Prof.  Abrams'  experiments  were  made  on  sacked  cement;  and  he 
intends  dupHcating  them  upon  cement  shipped  in  bulk.  Possibly  the 
result  of  the  new  tests  will  show  that  keeping  the  cement  in  large  masses 
will  postpone  somewhat  the  sudden  drop  in  strength  of  concrete  which 
occurs  with  cement  two  months  old.  It  would  be  interesting  to  learn 
what  the  loss  is  on  cement  one  month  old;  and  it  is  to  be  hoped  that  Prof. 
Abrams  will  add  to  the  value  of  his  very  useful  experiments  by  settling 
this  point. 

Protection  of  Fresh  Concrete 

The  protection  of  fresh  concrete  is  an  economic  matter,  as  far  as  the  con- 
tractor is  concerned,  because,  according  to  all  properly  drawn  specifications, 
he  will  have  to  make  good  at  his  own  expense  all  damage  done  to  the 
concrete  through  excessive  cold  or  heat,  or  any  other  cause,  before  the  final 
acceptance  of  the  finished  construction.  It  is  also  a  matter  of  economy  to 
the  owner,  because  if  the  concrete  is  at  all  damaged,  all  the  repairing  that 
the  contractor  may  do,  short  of  entire  removal  and  rebuilding,  will  fail  to 
make  the  job  as  good  and  satisfactory  as  it  would  have  been,  had  no  such 
misfortune  occurred. 

General  Remarks 

From  the  point  of  view  of  both  the  engineer  and  his  client,  it  is  truly 
economic  invariably  to  obtain  concrete  that  is  first-class  in  ever}'^  particu- 
lar— strong,  solid,  smooth,  and  hard — no  matter  how  much  it  may  cost; 
because  failure  of  any  kind  in  a  reinforced-concrcte  structure  is  likely  to 
be  both  serious  and  expensive.  Many  large  bridges  of  that  type,  which  were 
constructed  under  contracts  secured  through  competitive  bidding,  show 
after  a  few  years  signs  of  disintegration.  The  ultimate  result  of  such  work 
is  that  the  structure  sooner  or  later  will  require  cither  extensive  repairs  or 
entire  rebuilding.  The  causes  of  such  failures  may  be  attributed  to  objec- 
tionable methods  used  by  contractors  in  order  to  cheapen  the  cost  of  han- 


ECONOMICS  OF  CONCRETE  MIXING  395 

dling  and  depositing  the  concrete — such  as  chuting  it  long  distances,  using 
gravity  mixers,  allowing  insufficient  time  for  mixing,  putting  too  much  water 
in  the  mixture  so  as  to  avoid  most  of  the  expense  of  tamping  and  working 
the  aggregate  back  from  the  face  of  the  forms,  permitting  the  employment 
of  too  large  pieces  of  broken  stone  which  fail  to  pass  between  the  reinforcing 
bars,  laying  concrete  in  freezing  weather,  and  placing  concrete  under  water 
when  there  are  available  other  methods  which  would  permit  depositing  it 
in  the  air  at  a  httle  greater  cost. 

At  the  time  when  the  "  Final  Report  of  the  Joint  Committee  on  Concrete 
and  Reinforced-Concrete"  was  presented,  the  above  condition  prevailed, 
but  since  then  much  important  research  work  on  concrete  manufacture 
has  been  done,  and  there  are  now  several  publications  which  give  valuable 
data  and  point  the  way  to  better  concrete  structures — notably  the  records 
of  the  elaborate  series  of  experiments  made  by  Prof.  Duff  A.  Abrams.  But 
as  this  treatise  is  intended  to  cover  solely  the  field  of  economics  and  not 
that  of  general  engineering  practice,  the  reader  is  referred  for  further  data 
on  the  manufacture  of  proper  concrete  to  the  well-known  "Report"  before 
mentioned;  the  "Transactions"  of  the  American  Railway  Engineering  Asso- 
ciation, the  American  Society  for  Testing  Materials,  and  the  American 
Society  of  Civil  Engineers;  and  the  ''Bulletin"  of  the  Structural-Materials 
Research-Laboratory  of  the  Lewis  Institute. 

The  author  is  indebted  for  a  number  of  valuable  suggestions  on  concrete 
manufacture  to  his  friend,  J.  J.  Yates,  Mem.  Am.  Soc.  C.  E.,  Bridge  Engi- 
neer of  the  Central  Railroad  Company  of  New  Jersey,  and  Chairman  of 
the  Committee  on  Masonry  of  the  American  Railway  Engineering  Asso- 
ciation. 


CHAPTER  XL 

ECONOMICS   OF  ERECTION 

The  data  for  this  chapter  were  furnished  by  the  author's  old  friend, 
Frank  W.  Skinner,  Mem.  Am.  Soc.  C.E.,  who,  for  a  number  of  years,  made 
a  special  study  of  bridge  erection  in  all  its  details,  and  gave  the  results  of 
his  findings  in  numerous  lectures  to  engineering  students  of  the  leading  uni- 
versities and  technical  schools  of  this  country.  Much  of  the  valuable 
material  that  he  collected  was  published  in  Engineering  Record,  of  which 
paper  for  a  long  time  he  was  the  chief  editor  and  leading  spirit.  The 
author  feels  that  he  is  exceedingly  fortunate  in  obtaining  for  the  writing  of 
this  chapter  the  assistance  of  an  eminent  engineer  who  has  made  such  a 
thorough  study  of  bridge  erection  in  aU  its  ramifications.  There  are  very 
few  engineers  who  are  fitted  by  both  experience  and  temperament  to  dis- 
course scientifically  and  practically  concerning  the  essentially  specialized 
subject  of  the  economics  of  erection;  and  of  these  there  is  probably  not 
one  who  possesses  such  a  grasp  thereof  as  does  Mr.  Skinner.  What  follows 
is  given  as  closely  as  practicable  in  his  own  diction. 

The  erection  of  an  important  bridge  is  a  function  first  of  the  design, 
second  of  the  location,  and  third  of  the  available  equipment;  and  its  eco- 
nomics are  directly  related  to  these  fundamentals,  variations  in  which 
materially  influence  the  total  cost  of  erection  of  spans  of  the  same  length, 
the  same  carrying  capacity,  and  the  same  type.  The  recognition  of  these 
facts  has  been  such  that,  in  this  country,  the  art  of  bridge  erection,  particu- 
larly of  steel  spans,  has  been  highly  specialized — to  an  amount  comparable 
with  that  of  the  fabrication  of  bridge  superstructures  in  great  shops  fitted 
with  costly  tools  and  used  almost  exclusively  for  this  single  purpose.  It 
has  resulted  in  the  development  of  a  clearly-defined,  standard  practice  and 
the  perfection  of  a  number  of  methods  for  securing  essentially  the  same 
effects  under  different  conditions  and  with  different  appliances  arranged  to 
secure  the  maximum  safety  and  rapidity  with  the  mininunn  total  cost. 

These  methods,  and  the  special  equipments  that  have  been  devised  for 
them,  make  it  possible  for  a  given  structure  to  be  handled  in  several 
radically-different  ways,  which  may  either  show  in  some  cases  compara- 
tively-uniform 'results,  or,  generally,  will  indicate  a  decided  advantage  for 
one  method  over  all  the  rest. 

The  physical  and  mechanical  combinations  can  be  readily  analyzed 
so  as  to  give  a  limited  number  of  principal  cases  that  will  here  be  classified 

396 


ECONOMICS   OF   ERECTION  397 

for  the  general  and  comparative  economics,  so  that,  by  inteUigent  develop- 
ment and  modification,  they  will  cover  the  field  within  the  limits  of  justi- 
fiable construction. 

The  subjects  considered  are  divided  on  broad  lines  into  steel  and 
concrete;   long,  medium,  and  short  spans;   and  high  and  low  structures. 

Steel  Bridges 

As  far  as  possible  all  items  of  fabrication  should  be  completed  at  the 
bridge  shop,  so  as  to  reduce  the  amount  of  assembling,  fitting,  and  riveting 
in  the  field  to  a  minimum.  No  work  should  be  done  at  the  site  which  can 
be  performed  at  the  shop;  and  no  v/ork  should  be  done  on  the  structure 
itself  that  can  be  performed  ashore  upon  the  separate  or  combined  pieces 
before  erection.  Standard  plant  and  equipment  should  be  used ;  the  largest 
possible  proportion  of  work  should  be  done  by  machinery  and  power;  and 
the  most  skilful  and  experienced  labor  available  should  be  employed  in 
conformity  with  the  equation  of  the  different  costs  to  a  minimum  for  the 
completed  work,  including  salvage,  rental  of  plant,  cost  of  transportation, 
installation  and  removal  of  plant,  and  the  greater  or  less  importance  of 
extra  speed  (as  in  case  of  danger  from  floods),  always  considering  the  fun- 
damental requirements  for  absolute  safety  and  the  excellence  of  the  fin- 
ished work. 

It  is  assumed  that  the  methods,  plant,  equipment,  and  service  best 
adapted  to  the  type  of  structure  and  the  given  conditions  are  available, 
and  erection  with  them  wiU  be  considered  the  economic  method;  but  this 
decision,  of  course,  is  subject  to  modification  when  the  problem  is  compli- 
cated by  artificial  conditions  or  by  sudden  emergencies  that  make  changes 
of  details,  methods,  or  equipment  safer  or  more  practicable,  as,  for  instance, 
when  labor  troubles,  difficult  transportation,  scarcity  of  materials,  or  acci- 
dental physical  developments  make  the  original  preparation  susceptible  to 
delays  and  to  important  changes  of  conditions  that  may  have  a  vital 
influence  on  erection  operations;  and  radical  changes  in  the  original 
programme  are  sometimes  necessary,  in  order  to  prevent  large  increases  over 
the  proper  estiiiated  cost. 

Girder  Spans 

These  are  plate  girders  or  riveted  trusses  of  such  dimensions  that  they 
can  be  erected  complete  as  units,  usually  not  exceeding  50  or  60  tons  in 
weight,  100  feet  in  length,  and  15  feet  in  depth.  Even  these  Hmits  are 
likely  to  be  excessive  for  transportation  by  rail  from  the  fabricating  shop, 
the  size  generally  being  limited  by  bridge  and  tunnel  clearances  and  track 
curvature,  and  the  weight  by  twice  the  capacity  of  each  of  the  available 
cars. 

If  the  girders  can  be  shipped  entirely  by  water,  the  limits  for  trans- 
portation are  very  greatly  increased ;  and  under  special  circumstances  they 


398  ECONOMICS   OF  BRIDGEWORK  CkAPTER  XL 

may  be  equally  extended  for  erection.  Ordinarily  the  latter  is  a  very  simple 
process,  effected  by  one  or  by  two  derrick  cars  or  wrecking  cars  that  unload, 
transport,  and  erect  the  girders  in  position  in  single  or  successive  operations 
at  a  direct  cost  of  as  httle  in  pre-war  times  as  $1.00  per  ton. 

Derrick  cars  or  their  equivalent  are  not  always  available  in  remote 
locahties,  and  are  not  generally  possessed,  except  by  raih-oad  companies, 
bridge  companies,  and  important  contractors.  In  their  absence  the  girders 
can  be  handled,  usually  less  advantageously,  by  derricks,  gin-poles,  and 
various  combinations  of  jacking,  blocking,  rolling,  and  other  operations 
that  may  be  devised,  modified,  and  combined  according  to  the  experience 
and  ingenuity  of  the  erector;  and  although  theoretically  they  are  more 
expensive  and  less  efficient,  they  may  often  be  more  advantageous  than  the 
provision  of  high-class  equipment  under  disadvantageous  conditions. 

Viaduct  Erection 

Viaducts  generally  consist  of  two  or  more  lines  of  plate  or  lattice  girders 
from  30  to  100  feet  long  on  towers  up  to  100  feet  high,  although  these  dimen- 
sions have  been  considerably  exceeded  in  infrequent  cases.  The  ideal 
method  of  erection  is  by  means  of  a  derrick  traveler,  sometimes  called  a 
mule,  installed  at  grade  at  one  end  of  the  viaduct  and  having  a  reach  long 
enough  to  erect  one  tower  and  one  connecting  span  in  advance;  after  which 
it  moves  forward  on  the  completed  portion  of  the  structure,  erecting  panel 
after  panel  as  it  proceeds.  Such  travelers  have  at  least  two  main  booms  of 
great  length  and  one  or  more  auxiliary  booms  for  hoisting,  swinging,  and 
placing  the  steel  that  may  be  delivered  either  at  grade  or  on  the  surface  of 
the  ground.  With  a  large  number  of  duplicate  heavy  spans,  such  as  occur 
in  elevated  railroad  construction,  this  class  of  metalwork  can  be  erected  with 
great  rapidity,  a  record  of  1,000  lineal  feet  of  double-track  structure  per 
day  having  been  made  in  Brooklyn  with  one  traveler  and  crew,  independent 
of  the  preliminary  distribution  of  steel  and  the  subsequent  field  riveting. 

Where  the  girders  have  been  too  long  or  too  heavy,  or  the  towers  too 
far  apart  for  erection  with  a  boom  of  practicable  length,  cantilever  travelers 
have  been  successfully  employed.  They  have  been  of  different  types, 
usually  having  an  elevated  horizontal  boom  overhanging  the  wheel 
base  by  the  length  of  one  tower  span  and  one  connecting  span,  and  equipped 
with  trolley  hoists  for  unloading  material  from  cars  on  the  tracks  in  the  rear 
and  transferring  it  to  the  required  position  in  advance  for  assembHng  in 
the  structure. 

In  a  few  cases  where  there  has  been  a  great  length  of  viaduct  of  sub- 
stantially uniform  height  above  the  surface  of  the  levi^l  gromid,  the  struc- 
ture has  been  erected  by  a  strident  gantry  traveller,  moving  on  a  surface 
track  and  provided  with  several  sets  of  hoisting  tackles  to  handle  from  the 
ground  (where  they  were  distributed)  tlu^  span  and  tower  members. 


ECONOMICS   OF   ERECTION  399 

Medium  Spans 

Medium  spans  up  to  300  or  400  feet  long,  and  including  some  short 
spans,  when  for  any  reason  it  is  impracticable  to  handle  the  trusses  as  com- 
plete units,  are  generally,  in  the  case  of  new  work,  best  erected  on  ordinary 
framed  wooden  falsework  by  means  of  one  or  two  derrick  cars. 

When  there  are  pile  foundations  which  can  be  placed  in  advance,  the 
derrick  car  can  rapidly  put  in  the  framed-falsework  bents;  after  which  two 
derrick  cars,  one  at  each  end  of  the  span,  if  two  are  available,  can  place  the 
floor  system,  assemble  the  lower  chords,  erect  the  web  members  on  them, 
and  finish  the  erection  by  placing  the  top  chords,  top  laterals,  and  sway 
bracing  as  the  cars  retreat  from  the  center  to  the  ends  of  the  span. 

For  heavy  structures  where  the  top  chords  involve  too  great  a  load  for  a 
pair  of  derrick  cars,  or  where  locomotive  cranes  are  used  instead,  they  can 
be  supplemented  advantageously  by  a  simple  gantry  traveler  to  handle  the 
heaviest  members. 

It  is  entirely  practicable  to  execute  the  erection  wholly  with  the  gantry 
traveler;  but  that  traveler  is  costly  to  construct,  difficult  to  transport  from 
job  to  job,  and  rot  as  rapid  or  economical  as  derrick  cars  when  the  latter 
are  available. 

Alternative  Methods 

If  the  elevation  of  the  span  is  exceedingly  high  above  the  water;  if 
there  is  great  danger  from  ice  or  floods;  if  the  bottom  is  very  treacherous  or 
difficult;  if  the  current  is  too  fierce;  or  if  the  space  underneath  the  span 
must  not  be  obstructed  by  falsework  (as  when  it  is  required  to  be  left  open 
for  navigation  or  for  heavy  city  or  railroad  traffic  beneath),  falsework 
becomes  too  dangerous  or  expensive  or  is  wholly  inadmissible,  and  some 
other  system  of  erection  must  be  devised. 

The  most  common  method  is  by  cantilever  erection  from  each  end  of  the- 
span,  the  truss  members  being  made  heavier  or  temporarily  reinforced 
until  the  center-panel  connections  are  made  and  the  structure  is  trans- 
formed into  a  simple,  self-supporting  span.  This  method  involves  either 
the  provision  of  special  anchorages  and  counterweights  or  the  erection  of 
alternate  spans  in  advance  so  that  they  may  serve  as  anchorages.  Canti- 
lever erection  is  always  objectionable  when  it  can  be  avoided,  because  it 
is  much  slower  and  more  costly  than  falsework  erection,  and  as  there  is 
greater  danger  of  injury  to  the  uncompleted  structure  by  sudden  storms  or 
from  various  accidents  than  there  is  when  falsework  is  used. 

Sometimes  falsework  of  various  types  can  be  provided  eccentric  from 
the  alignment  of  the  bridge,  and  the  permanent  span  may  be  erected  on  it 
by  the  ordinary  method — then,  when  complete,  moved  transversely  to  the 
required  position  and  permanently  seated  on  the  substructure. 

The  method  of  protrusion  is  occasionally  employed  abroad  and  has  infre- 
quently been  adopted  in  America.     When  it  is  used,  the  span  is  erected 


400  ECONOMICS   OF   BRIDGEWORK  Chapter  XL 

complete  at  one  end  of  the  bridge  and  as  nearly  as  possible  at  the  requu-ed 
level,  the  rear  end  is  counterweighted,  and  (especially  if  there  is. only  a 
single  span)  the  forward  end  is  extended  by  a  temporary  pilot  truss,  when 
such  extension  is  necessary.  Each  span  is  pushed  forward  longitudinally  on 
roUers  until  the  forward  end  or  extension  takes  roller  bearing  on  the  next 
pier,  so  as  to  support  it  during  the  farther  advance  until  the  span  comes  to 
position  and  is  lowered  to  bearing.  If  several  spans  are  erected  in  the  same 
way,  they  are  temporarily  connected  to  form  a  continuous-girder  structure 
during  protrusion. 

Where  a  nmnber  of  spans  of  substantially  uniform  and  moderate  lengths 
are  constructed  in  one  bridge,  they  have,  under  certain  circumstances,  been 
erected  on  a  platform  suspended  from  a  temporary,  overhead,  movable 
span  that  travels  from  pier  to  pier  as  the  work  progresses. 

Where  the  ground  under  the  bridge  is  accessible,  unobstructed,  and  com- 
paratively level,  and  when  materials  can  be  delivered  there,  it  may  be 
possible,  as  has  occurred  in  some  cases,  to  distribute  the  steel  in  advance  at 
low  level,  erect  the  spans  there  complete  in  the  proper  alignment,  and  raise 
them  to  required  position  and  elevation  as  the  piers  are  built  up. 

Considerable  use  has  been  made  of  the  floating  method  whereby  the 
spans,  having  been  erected  in  the  usual  manner  on  shore  or  on  falsework 
built  in  comparatively  shallow  and  sheltered  waters,  have  been  transferred 
to  the  decks  of  scows,  towed  to  position  between  the  piers,  and  aligned  with 
their  seats  on  the  latter,  usually  at  low-level  elevation,  and  lowered  to 
place  by  the  use  of  water  ballast  or  tidal  fluctuations  or  both. 

In  very  difficult  and  unusual  conditions,  as  in  some  mountain  railroads, 
temporary  suspension  spans  have  been  built,  the  permanent  spans  erected 
on  them,. and  the  suspension  spans  removed. 

The  above  methods  and  their  combinations,  variations,  and  -modifica- 
tions have  all  been  successfully  used  on  different  occasions;  and  together 
they  cover  the  principal  features  of  ordinary  erection  for  medium,  long, 
and  short  spans.  Any  one  of  them  under  special  conditions  may  become 
the  economic  method  for  erection  in  that  case ;  but  where  it  is  practicable, 
the  method  of  erection  on  ordinary  falsework  with  a  derrick  car  or  traveler 
is  likely  to  be  most  desirable  and  economic. 

Long  Spans 

Up  to  about  700  feet  in  length  and  150  feet  in  clear  height,  spans  have 
been  erected  on  framcd-timber  falsework,  which,  of  course,  for  such  extreme 
dimensions  becomes  very  costly,  but  permits  more  rapid  and  satisfactory 
assembling  of  the  span  than  do  the  other  methods,  thus  making  presump- 
tion of  economic  desirability  for  this  method  when  it  can  be  used. 

The  very  fact  that  conditions  require  spans  of  more  than  400  feet  is 
quite  likely  to  indicate  deep  water,  bad  bottom,  swift  current,  great 
height,  or  wide,  unobstructed  openings  between  the  piers  that  will  make 
falsework  impracticable. 


ECONOMICS   OF  ERECTION  401 

In  such  cases,  as  in  medium  spans,  the  most  common  solution  is  erec- 
tion by  the  cantilever  method,  generally  counterbalancing  the  cantilever 
arms  from  previously-completed  portions  of  the  permanent  structure, 
building  both  cantilevers  of  the  same  spans  simultaneously,  and  connecting 
their  extremities  by  an  independent  suspended  span  designed  to  resist 
cantilever  stresses  developed  by  erection  and  to  function  subsequently  as 
a  simple  span. 

Cantilever  spans  have  been  erected  up  to  a  length  of  1,800  feet  with 
results  which  indicate  that  the  same  method  can  be  extended  to  lengths 
several  hundred  feet  greater.  Serious  consideration  has  been  given  to  the 
practicability  of  constructing  cantilever  spans  up  to  3,000  foet  in  length, 
which  length  approaches  the  present  limit  set  by  the  strength  of  materials; 
and  such  a  detailed  design  would,  of  course,  involve  the  development  of 
complete  cantilever-erection  plant.  In  this  case  it  is  probable  that  the 
assisted  cantilever  method  or  some  modification  of  it,  such  as  has  already 
been  adopted  in  some  large  cantilever  spans,  would  be  employed,  whereby 
temporary  supports  would  be  placed  under  the  cantilevers  between  the 
permanent  piers,  thus  greatly  reducing  the  erection  stresses. 

The  length  and  weight  of  the  members  of  the  suspended  trusses  in  a 
cantilever  span  necessitate  their  erection  by  a  heavy  traveler,  and,  if 
accomplished  by  the  cantilever  method,  produce  a  great  increase  of  the 
stresses  developed  by  the  erection  of  the  cantilever  arms  proper.  In  order 
to  avoid  these  stresses,  and  for  other  reasons,  the  suspended  span  has  in 
some  instances  been  erected  complete  at  a  low  level,  towed  to  position  under 
the  ends  of  the  finished  cantilever  arms,  hoisted  up,  and  connected. 

In  another  case  of  a  long-span  cantilever,  the  ends  of  the  cantilever 
arms  were  connected  by  a  light,  temporary  suspension  bridge  on  which 
the  permanent  suspended  span  was  erected. 

The  difference  in  local  conditions,  type,  and  other  features  may  make 
any  one  of  these  methods  the  most  economic  one  for  the  given  case,  so 
that  for  an  extremely  large  structure,  all  of  them  wiU  probably  have  to  be 
analyzed  for  the  final  comparative  determination. 

Suspension  Beidges 

Short-span  and  temporary  suspension  bridges  may  be  designed  with 
main  cables,  each  composed  of  one  or  more  twisted  wire  ropes  extending 
continuously  from  anchorage  to  anchorage,  that  can  be  dehvered  complete 
at  the  site,  and,  with  ordinary  appliances,  pulled  across  the  river  from 
tower  to  tower  and  from  tower  to  anchorage,  secured  in  place,  and  adjusted, 
after  which  the  erection  fron^  them  of  the  remainder  of  the  superstructure 
is  comparatively  simple  and  easy.  Generally  this  is  the  most  economic 
method. 

For  all  long-span  suspension  bridges,  the  universal  method  of  erection 
has  been  the  preliminary  construction  of  falsework  suspension  bridges, 


402  ECONOMICS   OF  BRIDGEWORK  Chapter  XL 

erected  as  described  for  short-span  and  medium  suspension  bridges,  and 
their  use  as  suspended  falsework  for  the  construction  of  the  main  cables 
built  up  from  straight  wires  spliced  to  form  continuous  lines  reaching 
around  and  around  the  anchorage  pins  and  adjusted  to  the  proper  catenary 
curve  and  elevation  as  they  are  successively  laid.  These  are  grouped  first 
into  strands  and  then  into  the  main  cables;  and  the  stiffening  trusses  and 
the  roadways  are  erected  on  them  by  means  of  simple  travelers. 

Suspension  bridges  having  eye-bar  chains  could  be  erected  in  a  similar 
manner  from  a  temporary,  suspension-falsework  platform. 

Arch  Spans 

Very  short  arch-spans  should  be  erected  like  girder  spans,  and  handled 
as  units  by  any  convenient  apparatus.  Medium  and  long  spans  are  gen- 
erally erected  on  falsework  or  by  the  cantilever  method.  As  in  the  case  of 
ordinary  truss  spans,  erection  on  falsework  is  economic  when  practicable; 
and  for  arches  of  the  plate-girder  or  solid-rib  type  this  method  can  hardly 
be  replaced  by  any  other,  when  the  spans  are  of  any  considerable  length. 
Care  must  be  taken,  however,  to  brace  the  falsework  thoroughly  so  as  to 
resist  the  oblique  stresses  and  thrusts  that  are  produced  by  unequal  loading 
as  the  inclined  sections  of  girders  are  assembled,  unless  particular  pains  are 
taken  to  arrange  them  so  as  to  maintain  balanced  reactions  throughout 
the  erection.  Plate-girder  arch-spans  up  to  510  feet  long  have  been 
erected  on  falsework. 

Truss  arch-spans  may  be  erected  by  the  cantilever  method,  which  has 
been  employed  successfully  for  most  of  the  large  spans  and  up  to  the 
greatest  present  maximum  of  about  1,000  feet  clear  opening.  'By  this 
method  the  top  chords  of  the  semi-spans  which  are  built  simultaneously 
are  tied  back  to  sufficient  anchorages  with  adjustable  connections  so  that 
the  spans  may  be  revolved  around  their  skewback  hinges  in  order  to  make 
the  center  connection  at  the  crown. 

Erection  Plant 

A  very  important  feature  in  the  economics  of  bridge  erection  is  the 
design  and  operation  of  the  special  plant  provided  for  handling  the  heavy 
members  in  the  field.  It  has  been  found  good,  economic  practice  to  expend 
large  sums  in  the  construction  of  plant  for  the  erection  of  a  single  structure, 
and  for  the  equipment  of  the  field  force  with  special  machinery  and  ]iower 
appliances  of  great  capacity.  This  apparatus  is  so  costly  that  none  but  the 
most  important  construction-companies  keep  it  in  stock;  and  the  existence 
of  available  plant  of  this  nature  is  often  an  important  factor  in  the  design 
of  the  stnu^turc  and  in  the  award  of  the  construction  contract.  Among  the 
important  standard  appliances  for  bridge  erection  are  derrick  cars,  derricks, 
hoisting  engines,  and  riveting  machinery  that,  in  general,  are  applicable  for 


ECONOMICS   OF   ERECTION  403 

all  very  large  jobs,  and  may,  therefore,  constitute  a  part  of  the  regular 
equipment,  the  same  as  do  the  tools  in  the  fabricating  shop. 

The  cost  of  their  transportation,  installation,  and  removal  is,  however, 
a  special  feature  that  must  be  considered  in  the  determination  of  the  eco- 
nomics of  each  structure.  For  very-long-span  trusses  there  are  necessary- 
enormous  steel  travelers  that,  with  their  equipment,  may  sometimes 
weigh  1,000  tons;  and,  when  the  job  is  finished,  they  are  hkely  to  be  unsuit- 
able for  future  work  and  of  comparatively  small  value  for  salvage. 

For  very  heavy  work  it  is  also  necessary  in  some  cases  to  provide 
structural-steel  falsework  and  to  employ  considerable  ingenuity  in  its  con- 
struction from  portions  of  the  permanent  structure  afterwards  to  be 
erected.  The  repeated  use  of  special  erection-metal  and  its  availability  for 
other  purposes  after  the  finishing  of  the  job  are  important  elements  in  the 
economics  of  the  problem. 

As  the  principal  members  of  long  spans  have  attained  a  maximum 
weight  of  more  than  100  tons  each,  it  has  been  necessary  to  provide  special 
methods  of  handling  them  and  of  securing  them  to  the  hoisting  apparatus; 
and  considerable  sums  have  been  spent  in  the  construction  of  steel  yokes, 
clamps,  beams,  and  other  special  devices  intended  solely  to  provide  rapid 
and  effective  connections  to  these  pieces  and  to  enable  them  to  be  accurately 
and  safely  handled.  Such  appliances  greatly  reduce  the  amount  of  hand 
labor  and  justify  considerable  preliminary  expenditure. 

Replacing  Steel  Bridges 

The  replacement  of  steel  bridges  almost  always  involves  the  mainte- 
nance of  traffic  on  the  bridge  and  often  of  navigation  below  the  structure 
during  the  process  of  reconstruction.  In  most  cases  the  new  structure  is 
on  the  same  alignment  and  nearly  or  quite  at  the  same  elevation  as  the  old 
one;  and  frequently  the  old  substructure  is  satisfactory  with  minor  modi- 
fications to  receive  the  new  superstructure.  It  is  often  difficult,  and  some- 
times very  expensive,  to  divert  the  traffic  from  the  old  structure  while  the 
new  one  is  being  erected;  hence  the  problem  of  reconstruction,  especially 
of  long  and  high  spans,  thus  becomes  one  of  the  most  difficult  and  expensive 
that  are  likely  to  be  encountered,  and  the  economics  vary  so  greatly  that 
no  general  determination  can  be  made,  necessitating  that  they  be  investi- 
gated independently  for  each  structure. 

For  short  spans  where  the  whole  span  or  its  single  complete  girders  or 
trusses  can  be  handled  as  units  by  travelers,  derrick  cars,  or  other  apparatus 
traveUng  on  the  ground  alongside,  or  on  the  structure  itself,  and  especially 
where  the  bridge  is  a  double-track  railroad  structure,  it  is  usually  compara- 
tively easy  to  divert  traffic  to  one  track,  and  to  remove  the  old  structure 
piecemeal,  putting  in  the  new  parts  as  fast  as  the  old  ones  are  taken  out  and 
gradually  rebuilding  the  entire  superstructure. 

For  viaducts  this  may  frequently  be  done  with  two  derrick  cars  handUng 


404  ECONOMICS   OF  BRIDGEWORK  Chapter  XL 

the  girders  together,  one  at  each  end,  provided  the  towers  do  not  need 
removal ;  but  in  the  latter  case,  particularly  if  the  viaduct  is  very  high  and 
the  connecting  spans  are  long,  the  problem  becomes  one  of  great  difficulty 
and  expense. 

This  replacement  can  be,  and  has  been,  accompUshed  by  supporting  the 
structure  on  falsework;  by  suspending  it  from  overhead  spans  long  enough 
to  reach  from  tower  to  tower,  and  carrying  successively  both  old  and  new 
structures;  and  by  providing  new  towers,  or  portions  of  new  towers,  before 
the  old  towers  are  wholly  or  partly  removed. 

All  of  these  methods  are  hkely  to  be  slow,  hazardous,  and  expensive; 
and  they  must  be  very  carefully  plaimed  in  detail  for  each  structure  con- 
sidered. 

When  the  old  and  the  new  structures  can  successively  support  each 
other  during  the  construction,  or  when  it  is  possible  to  by-pass  the  traffic, 
or  to  transpose  old  and  new  structures  transversely  in  sections,  or  when  it 
is  possible  to  build  new  towers  intermediate  between  the  old  ones  or  adja- 
cent to  them,  the  difficulties  are  likely  to  be  considerably  diminished,  but 
such  favorable  conditions  do  not  frequently  prevail. 

As  the  economics  of  design  necessitate  a  rapid  increase  of  span-lengths 
and  weight  with  increasing  height  of  track,  the  units  handled  in  recon- 
structing a  high  viaduct  become  very  large,  and  the  derrick-car  method 
and  the  translation  of  the  structure  as  a  whole  are  likely  to  be  impracticable. 

Replacing  Short  Spans  on  Old  Substructure 

Several  methods  of  replacement  of  short  and  medium-length  spans  have 
been  devised  and  repeatedly  executed  until  they  are  to  a  certain  degree 
standardized;  and  under  ordinary  conditions  they  may  frequently  be 
selected  by  inspection  and  modified,  if  necessary,  to  suit  the  special  condi- 
tions and  requirements  of  the  case.  Under  such  circumstances  the  method 
that  provides  the  most  simple  and  rapid  operations  with  the  least  temporary 
construction  is  likely  to  be  the  most  economic. 

Where  the  spans  are  over  water  that  is  not  too  swift  nor  too  much 
obstructed,  and  where  navigation  permits,  it  is  frequently  possible  to  place 
both  the  old  and  the  new  span  on  barges  or  theh  equivalents,  and,  at  the 
given  time,  disconnect  the  old  span  from  its  original  support  and  carry  it 
immediately  transversely  out  of  position,  and  sinuiltaneously  or  succes- 
sively move  the  new  span  into  the  former  position  of  the  old  one,  seating  it 
on  its  permanent  foundations,  the  old  span  being  removed  to  any  suitable 
location.  This  system  is  frequently  used  for  drawbridges;  and  under 
favorable  circumstances  the  entire  operation  can  be  concluded  with  only  a 
very  short  interruption  to  traffic  on  the  structure.  The  spans  are  usually 
raised  and  lowered  by  regulating  the  amount  of  water  ballast  in  the  barges. 

Replacing  by  transverse  displacement  has  been  successfully  accom- 
plished for  spans  up  to  200  feet  or  more  in  length.     By  this  method  the 


ECONOMICS   OF   ERECTION  405 

new  span  is  completely  erected  as  close  alongside  the  old  span  as  possible, 
and  the  floor  is  placed  on  it  ready  for  traffic.  Upper  and  lower  sets  of  track- 
rails,  transverse  to  the  bridge  axis  and  extending  completely  under  and 
beyond  both  the  old  and  the  new  span,  are  placed  beneath  the  ends  of  both 
spans,  and  are  separated  by  live  rollers.  Both  the  old  and  the  new  span 
are  seated  on  the  upper  track-rails  and  are  moved,  usually  simultaneously, 
transversely  until  the  old  span  is  carried  clear  of  the  alignment,  the  new  span 
following  it  up  until  it  occupies  the  required  permanent  position,  when  it  is 
lowered  to  its  masonry  seat  and  the  old  span  is  dismembered  and  removed. 
The  operations  are  accomplished  with  hydraulic  jacks  and  power  tackles; 
and  the  work  can  sometimes  be  done  so  rapidly  as  to  involve  only  a  few 
minutes'  interruption  to  traffic.  The  rapidity  of  the  work  is  often  an 
important  economic  consideration  that  may  outweigh  considerable  extra 
expense  in  the  way  of  labor,  material,  and  equipment. 

For  spans  of  more  than  100  feet,  it  is  often  desirable  to  support  the  old 
span  on  falsework  that  is  designed  also  to  carry  the  new  span  during  erec- 
tion, and,  after  the  removal  of  the  old  trusses,  to  erect  the  new  span  on  the 
falsework,  frequently  while  the  traffic  is  carried  on  the  old  floor  that  is  still 
supported  by  the  said  falsework. 

If  the  old  span  is  strong  enough  to  sustain  the  new  span  during  con- 
struction, plus  the  weight  of  the  minimum  traffic  necessary,  the  new  span 
may  be  so  designed  as  to  permit  its  construction  by  this  method;  and,  after 
■  completion,  it  may,  if  necessary,  be  moved  a  short  distance  either  horizon- 
tally or  vertically,  in  order  to  bring  it  into  the  exact  ahgnment  after  the 
old  structure  has  been  removed. 

In  other  cases  the  new  span  may  be  designed  with  transverse  dimensions, 
greater  than  those  of  the  old  structure,  that  enable  it  to  be  built  outside  of 
the  latter  and  practically  independent  of  it,  so  that  the  new  construction 
may  be  substantially  completed  while  traffic  is  maintained  on  the  old 
structure;  after  which  it  will  receive  traffic  and  will  support  it  and  the 
weight  of  the  old  structure  whilst  the  latter  is  removed  piece-meal. 

Replacing  Long  Spans 

Comparatively  few  very-long  spans  have  been  replaced  by  new  ones  in 
the  same  alignment.  The  principles  governing  the  operation  are  sub- 
stantially those  developed  for  moderate-length  spans,  with  the  exception, 
perhaps,  of  the  application  of  the  cantilever  method,  by  which  the  trusses 
of  new  long  spans  have  been  built  out  as  cantilever  arms  which  clear  the 
old  structure  and  are  self-supporting  during  erection. 

If  traffic  can  be  diverted  from  the  old  structure  during  its  replacement, 
the  old  trusses  will  be  likely  to  be  found  strong  enough  to  support  the  new 
span  during  erection;  and,  if  there  are  more  than  two  lines  of  trusses, 
the  old  ones  may  be  successively  replaced  by  the  new  ones. 

In  the  case  of  a  suspension  bridge,  the  factor  of  safety  of  the  cables  is 


406  ECONOMICS   OF   BRIDGEWORK  Chapter  XL 

such  that,  if  well  designed,  they  are  likely  to  outlast  the  roadwaj^  and 
trusses,  consequently  the  latter  can  easily  be  replaced  without  other  support 
than  that  afforded  by  the  cables  themselves. 

For  spans  approaching  the  present  limits  of  lengths,  the  necessary 
practice  is  for  such  efficient  construction,  capacity,  and  maintenance  that 
there  is  little  prospect  of  any  need  for  replacement  of  the  superstructures; 
and,  should  it  become  necessary,  there  would  probably  be  little  choice  of 
methods.  Any  scheme  that  would  be  possible,  however,  should  be  entitled 
to  favorable  consideration. 

Erection  of  Concrete-Girder  Bridges 

Concrete-girder  bridges  are  usually  concreted  in  situ  by  ordinary  meth- 
ods and  with  standard  equipment  involving  regular  operations  that  do  not 
present  any  special  economic  features.  There  may,  however,  be  a  decided 
economic  consideration  in  the  question  of  using  pre-cast  members  for  such 
structures.  The  large  capacity  of  derrick  cars  and  of  other  equipment 
that  is  available  makes  it  possible  in  some  cases  to  cast  long  girders  and 
heavy  floor  slabs  in  multiple,  in  the  Contractor's  yard,  remote  from  the 
bridge  site  and  under  conditions  more  favorable  to  good  work  and  eco- 
nomical operation  than  those  existing  at  the  latter,  and  afterwards  to 
transport  the  well-seasoned  units  to  position  and  set  them  in  place  ready 
for  service.     This  method  is  especially  applicable  to  railway  structures. 

The  economic  considerations  are  likely  to  involve  not  only  freight  cost 
but  also  quality  of  structure  and  rapidity  of  operations  as  affecting  the 
interruption  of  traffic. 

Concrete  Arch  Spans 

Arch  spans  must  be  concreted  in  situ  on  forms  rigidly  supported  against 
settlement  and  provided  with  devices  for  striking  the  center  so  as  to  swing 
the  arch  free  of  its  construction  support  when  the  concrete  has  sufficiently 
hardened.  For  short  spans,  low  heights,  and  where  obstructions  under- 
neath are  permissible,  the  forms  can  usually  be  most  economically  sup- 
ported on  ordinary  falsework-bents. 

Where  the  height  is  great,  or  where  passage  must  be  maintained  under- 
neath for  stream  flow,  navigation,  or  traffic,  it  is  often  necessary  to  carry 
these  forms  on  arch-center  trusses.  For  short  spans  these  may  be  of  cither 
timber  or  steel;  but  for  medium  and  long  spans  they  are  almost  always 
constructed  of  riveted  st(H^lwork,  usually  arranged  in  sets  braced  together 
and  often  moved  transversely  from  side  to  side  of  a  wide  bridge  and  longi- 
tudinally from  span  to  span  as  the  work  progresses,  thus  making  one  set 
suffice  for  many  places. 


CHAPTER  XLI 

Economics  of  Maintenance  and  Repairs 

Although  in  years  long  gone  by  the  author  did  considerable  work  in 
the  line  of  examination  and  repairs  of  old  bridges,  he  feels  that  he  can  no 
longer  consider  himself  an  expert  therein.  It  is  a  case  of  tempora  mutantur; 
for  the  methods  employed  today  in  bridge  repairing  are  essentially  different 
from  those  that  were  in  vogue  some  two  or  three  decades  ago.  For  this 
reason  the  author  appealed  to  several  old  friends  in  his  specialty,  who  are 
authorities  in  this  class  of  work,  to  furnish  him  data  for  the  writing  of  this 
chapter.  Several  of  them  generously  complied  with  his  request,  viz.,  Mr. 
Chas.  F  Loweth,  Chief  Engineer  and  formerly  Bridge  Engineer  of  the 
Chicago,  Milwaukee,  and  St.  Paul  Railway  System,  Mr.  Carl  S.  Heritage, 
Bridge  Engineer  of  the  Kansas  City  Southern  Railway  Company,  of  which 
line  the  author  is,  and  for  some  two  decades  has  been,  the  Consulting 
Engineer,  and  Messrs.  J.  G.  Chalfant  and  V.  R.  Covell,  respectively  County 
Engineer  and  Deputy  County  Engineer  of  the  County  of  Allegheny, 
Penna.  For  their  truly  valuable  aid  the  author  desires  to  extend  to  these 
gentlemen  his  hearty  thanks  and  his  deep  appreciation  of  their  kindness  and 
courtesy. 

A  rule  of  practice  which  the  author  established  for  his  own  guidance 
fully  a  quarter  of  a  century  ago  seems  to  have  found  favor  with  the  pro- 
fession, viz.,  that  any  old  bridge,  which,  in  either  main  members  or 
details,  would  be  overstressed  by  the  actual  live  loads  passing  across  it,  or 
likely  soon  to  traverse  it,  not  more  than  fifty  per  cent  in  excess  of  the 
standard  intensities  of  working  stresses  employed  in  designing  new  struc- 
tures, may  safely  be  allowed  to  remain  in  use.  If  overstressed  much  more 
than  this,  it  should  be  removed  and  employed  at  some  other  location  where 
the  traffic  is  light,  or  else  scrapped.  Exception  was  made  in  the  case  of 
plate-girder  spans;  for  these  could  be  relied  upon  to  give  ample  warning  of 
failing  strength  by  rivets  working  loose.  A  plate-girder  span  when  greatly 
overloaded  will  not  collapse  suddenly  as  will  a  pin-connected  or  even  an 
open-webbed-riveted  span. 

A  favorite  economic  expedient  of  the  author's  used  to  be  to  convert  two 
old  duplicate  bridges  into  one  and  put  in  a  new  one  at  the  crossing  left 
vacant.  This  scheme  was  specially  applicable  on  long  lines  of  railway 
where  standard  I-beam  and  deck-plate-girder  spans  were  used. 

The  more  crudely  a  bridge  was  designed  the  more  difficult  it  is  to  rein- 

407 


408  ECONOMICS   OF  BRIDGE  WORK  Chapter  XLI 

force  it  so  as  to  make  it  carry  satisfactorily  heavier  loads  than  those  for 
which  it  was  proportioned.  In  fact,  the  character  of  detaihng  employed 
previous  to  the  nineties,  in  which  decade  the  science  of  bridge  design  began 
to  be  estabhshed,  was  so  outrageously  unscientific  as  to  lead  the  author  to 
suggest  the  axiom  that  "the  best  way  to  repair  an  old  bridge  is  to  throw  it 
into  the  scrap  heap  and  build  a  new  one." 

Quite  often  bridges  are  repaired,  which,  from  the  standpoint  of  true 
economy,  should  be  relegated  to  the  discard.  One  such  case  of  some 
importance  occurred  in  the  author's  practice  in  the  late  eighties.  It  was  an 
old  Post  Truss  bridge  across  the  Missouri  River  at  Fort  Leavenworth, 
Kansas,  which  had  been  seriously  injured  by  the  burning  of  a  large  portion 
of  the  wooden  floor.  The  total  cost  of  the  repairs  was  somewhat  in  excess 
of  one  hundred  thousand  dollars — an  amount  greater  than  the  sum  total  of 
all  the  subsequent  incomes  from  both  railway  and  highway  traffic.  In 
extenuation  of  his  action  in  repairing  this  structure,  the  author  might 
mention  the  fact  that  he  was  not  consulted  about  the  economics  of  the 
case  or  the  advisability  of  repairing,  but  was  simply  given  the  job  of  engi- 
neering the  reconstruction  of  the  damaged  structure.  However,  he  is  not 
sure  that,  at  that  stage  of  his  career  and  in  those  days  of  primitive  bridge 
design  and  construction,  his  judgment  was  far  enough  developed  to  enable 
him  to  come  to  a  truly  economic  decision,  had  the  problem  of  the  economics 
of  the  case  been  submitted  to  him. 

The  method  of  solving  such  a  problem  is  to  estimate  upon  a  liberal  basis 
the  probable  cost  of  the  repairs,  and  upon  a  conservative  basis  the  probable 
duration  of  life  of  the  repaired  structure,  also  the  probable  costs  of  an  entirely' 
new  bridge  both  at  the  date  of  consideration  and  at  the  expiration  of  the 
said  life.  If  the  latter  cost,  plus  the  cost  of  the  repairs  with  compound 
interest  thereon  up  to  the  time  of  the  renewal,  plus  the  net  cost  of  removal  of 
old  structure  (i.e.,  cost  of  the  work  less  scrap  value)  is  smaller  than  the  net 
cost  of  immediate  removal,  plus  the  cost  of  a  new  structure,  built  imme- 
diately, plus  compound  interest  on  the  sum  of  these  two  costs  at  the 
assumed  later  date,  plus  the  small  value  of  the  deterioration  of  the  new 
structure  in  the  interval  between  the  said  two  dates,  then  the  repairs  will 
be  warranted. 

It  is  evident  that  the  correct  determination  of  the  answer  to  any  such 
economic  question  demands  wide  experience,  sound  judgment,  correct 
vision,  and  a  practical  acquaintance  with  the  theory  of  economics. 

In  the  old  days  a  large  portion  of  the  work  of  bridge  examination  and 
repairing  fell  to  the  lot  of  the  consulting  engineers;  but  such  now  is  far 
from  being  the  case,  because  it  is  only  for  very  large  and  important  struc- 
tures, or  those  having  moval)lc  spans  of  a  complicated  character,  that  the 
independent  specialists  arc  retained  on  repairs  and  roconstruc^tion.  Such 
work  is  ordinarily  done  by  the  bridge  engineers  regularly  employed  by  the 
raih'oads,  the  states,  and  the  municipalities;  and  these  men  have  become 
exceedingly  expert  therein. 


ECONOMICS   OF   MAINTENANCE   AND   REPAIRS  409 

So  much  for  the  author's  views  upon  the  subject  under  consideration; 
and  now  for  those  of  his  before-mentioned  friends. 

In  respect  to  Mr.  Loweth's  contribution  to  this  symposium,  on  Feb.  6, 
1920,  he  wrote  as  follows: 

My  Dear  Dr.  Waddell, 

Replying  to  your  inquiry  regarding  "Bridge  Maintenance  and  Repairs,"  I  would 
refer  you  to  a  paper  which  was  somewhat  hurriedly  written  in  the  fall  of  1918  for  the 
annual  convention  of  the  American  Railway  Bridge  and  Building  Association,  entitled 
"Carrying  Bridges  Over,"  and  which  covers  in  general  the  matters  referred  to  in  your 
letter.  This  paper  was  written  during  the  stress  of  war  times  when  steelwork  was 
very  difficult  to  get  and  the  need  of  economies  was  urgent;  hence  it  was  necessarily 
quite  hastily  prepared,  and  I  feel  that  for  usual  conditions  the  views  expressed  therein 
should  in  some  respects  be  modified. 

My  experience  on  this  road  *  has  been  generally  one  in  which  it  was  comparatively 
easy  to  take  care  of  the  replacement  of  the  lighter  bridges.  We  have  a  great  many 
branch  lines  on  which  the  traffic  is  necessarily  light  and  where  in  many  cases  it  will 
always  remain  so.  There  was  little  loss,  therefore,  in  taking  a  light  bridge  out  from  a 
first-class  line  and  placing  it  in  a  second-class  or  third-class  line  where  it  would  serve 
just  as  useful  a  purpose,  at  least  for  many  years,  as  a  bridge  of  the  heaviest  classification. 

To  do  this  involved  charges  to  Capital  Account  on  the  lighter  lines.  During  wai 
times  we  were  not  in  a  position  to  assume  the  charges  to  Capital  for  improvement  of 
the  said  lighter  lines;  and  the  difficulties  of  getting  new  steelwork,  to  say  nothing  of  the 
very-rapidly-increasing  cost,  resulted  in  a  new  condition,  hence  we  looked  into  the 
matter  of  strengthening  bridges  in  place  more  fully  than  we  had  done  previously,  with 
the  result  that  we  did  more  of  that  work  than  we  had  even  thought  of  doing  before  that 
time.  All  of  this  work  was  not  uniformly  satisfactory,  as  you  can  readily  see,  because 
some  structures  did  not  easily  lend  themselves  to  strengthening  in  a  manner  at  all  suit- 
able from  the  designer's  standpoint;  but  by  the  exercise  of  judgment  and  some  courage, 
and  at  the  same  time  by  ignoring  some  of  the  refinements  of  calculation,  we  arrived  at 
results  that  produced  economies,  or  what  may  be  equally  important,  the  deferring  of 
major  expense  even  at  the  loss  of  ultimate  economy. 

The  curse  of  the  poor  is  their  poverty,  and  the  railroads  have  sometimes  been,  and 
to  a  large  extent  are  now,  in  the  position  where  present  economy  is  perhaps  more  to  be 
considered  than  ultimate  economy. 

Just  as  an  illustration  of  what  we  are  up  against,  we  have  on  one  of  our  second  or 
third-class  lines  four  rather  large  bridges  which  have  been  carried  to  their  limit.  The 
substructures  are  very  old  and  small,  and  the  superstructures  also  are  quite  old.  It  is 
an  exceedingly  difficult  matter  to  strengthen  them — in  fact,  we  can  only  hope  to  remove 
the  most  glaring  defects;  and  anything  we  can  do  in  that  line  will  permit  of  using 
only  sUghtly  heavier  power  than  the  quite-Hght  power  now  being  operated  over  that 
division. 

Our  program  for  strengthening  would  involve  a  cost  of  about  $74,000.  To  replace 
the  bridges  with  new  structures  would  require  probably  more  than  $600,000.  It 
seems  too  bad  to  spend  so  large  a  sum  on  these  old  structures;  but  assuming  that  we 
could  carry  them  along  safely  for  only  four  years,  that  would  make  an  annual  cost  of 
only  $18,500,  exclusive  of  interest,  and  we  should  have  saved  an  expenditure  of  over 
$500,000,  the  interest  on  which  would  amount  to  at  least  $30  000  a  year.  In  this 
instance  a  new  structure  could  be  credited  with  a  considerable  amount  for  the  greater 
safety  and  other  considerations  incident  to  the  better  bridge,  but  I  think  we  shall  have 
to  decide  favorably  on  the  extraordinary  repairs  for  what  will  probably  be  but  a  short 
period  of  usefulness. 


*  Chicago,  Milwaukee,  &  St.  Paul  Railway  System. 


410  ECONOMICS   OF  BRIDGEWORK  Chapter  XLI 

We  are  now  aiming  to  restrict  fiber  stresses  ia  all  structures  to  the  lower  limit 
indicated  in  the  paper,  with  the  understanding  that  some  features  of  the  design  or  other 
conditions  may  make  even  this  lower  Umit  inadmissible  and  vice-versa. 

The  more  important  parts  of  the  paper  mentioned  are  as  follows: 

General  Considerations 

In  the  maintenance  of  bridges  there  are  two  general  considerations  to  be  observed: 

1.  Safety  in  carrying  the  necessary  traffic. 

2.  Economy — i.e.,  obtaining  the  maximmn  hfe  from  the  structure  at  reasonable 
maintenance  cost. 

On  all  railroads  which  are  twenty-five  or  more  years  old,  there  are  usurHy  a  number 
of  light-capacity  bridges  which  impose  more  or  less  restrictions  on  the  train  loadings 
that  can  be  handled  over  the  lines.  This  is  a  very  serious  problem  on  railroads  which 
have  many  bridges  that  were  built  during  the  eighties  and  early  nineties. 

New  bridges  are  generally  designed  for  the  heaviest  engine  and  car  loadings  in 
existence  at  the  time.  In  proportioning  them  there  is,  however,  a  certain  margin  between 
the  unit  stresses  which  are  used  and  the  maximum  unit  stresses  which  the  material 
can  safely  carry.  This  margin  provides  an  allowance  for  some  future  increased  engine 
and  train  loadings,  in  addition  to  the  contingencies  which  are  usually  embraced  by 
the  term  "  factor  of  safety." 

Classification  of  Bridges 

The  term  "Classification  of  Bridges  "  is  used  to  describe  the  systematic  investigation 
of  fight-capacity  bridges,  with  the  view  to  determining  the  maximum  loads  which  can 
safely  be  carried. 

Formerly,  the  common  practice,  when  a  new  engine  loading  was  up  for  consider- 
ation, was  to  investigate  aU  of  the  light  bridges  on  the  lines  where  the  use  of  the  heavy 
loading  was  contemplated.  Stresses  throughout  the  structures  for  this  loading  were 
figured,  and  decision  then  made  by  the  one  responsible  for  the  said  structures  as  to 
whether  the  load  could  be  safely  handled.  Each  time  a  new  loading  came  up  for  con- 
sideration the  process  was  repeated;  and  Uttle  or  no  use  was  made  of  the  previous  com- 
putations. 

The  present  practice  on  the  C.  M.  &  St.  P.  Ry.  is  to  make  an  investigation  or 
"classification"  of  each  structure.  Its  carrying  capacity  is  determined  in  terms  of  a 
standard  series  of  train  loadings.  New  engine  and  car  loadings  that  come  up  for  con- 
sideration are  classified  in  the  same  series  of  standard  loadings,  and  it  is  then  a  matter  of 
direct  comparison  to  tell  whether  such  proposed  loadings  can  be  safely  handled  over  the 
various  bridges.  Every  bridge  whose  date  of  construction  indicates  that  it  is  of  light 
design,  or  which  is  known  to  be,  or  suspected  of  being,  overloaded,  is  thus  classified. 
Every  part  of  the  structure  is  figured  or  taken  into  consideration. 

In  making  these  classifications  it  is  necessary  first  of  all  to  establish  the  maximum 
unit  stresses  to  which  the  various  materials  can  safely  be  subjected.  For  the  different 
materials  these  maximum  safe  stresses  are  taken  as  near  the  limit  of  strength  of  the 
material  as  is  considered  safe.  The  maximum  safe  stresses  must  be  assumed  low 
enough  so  that  there  is  no  danger  of  the  material  yielding,  altering  its  character,  or 
reducing  its  strength  for  carrying  loads  after  being  subjected  to  this  limiting  stress  for 
any  number  of  times. 

As  an  illustration  of  what  may  be  considered  as  safe  limiting  unit  stresses,  the 
following  are  given,  and  may  be  taken  to  api)ly  where  the  design  and  physical  condi- 
tion of  the  structure  arc  known  to  be  first-class: 


ECONOMICS   OF  MAINTENANCE   AND   REPAIRS 


411 


Poimds  per  Square  Inch 

Wrought  Iron 

Steel 

Beams  and  girders,  fiber  stress  in  bending 

22,000 
20,000 

2,000 

26,000 

Truss  members,  tension  on  net  section 

24,000 

Timber  stringers,  fiber  stress  in  bending  (with  suitable 
reduction  for  age  in  the  case  of  exposed  timber  over  six 
or  eight  years  old) 

In  fixing  upon  limiting  unit  stresses  for  loading  old  bridges,  it  is  necessary  to  take 
into  account  the  following: 

Character  of  design;  that  the  details  are  well  proportioned  and  direct  in  action, 
and  that  there  is  no  ambiguity  or  uncertainty  as  to  how  the  members  act. 

Character  of  the  workmanship  entering  into  the  structure  as  indicated  by  the 
reputation  of  the  makers  and  by  any  material-test  data  that  may  be  available. 

Deterioration. 

Action  under  load,  such  as  rigidity  and  freedom  from  excessive  vibration. 

Speeds  likely  to  obtain  over  the  structure,  and  confidence  as  to  the  observance  of 
any  speed  restrictions  that  may  be  imposed. 

Element  of  certainty  as  to  the  assmned  loading  being  the. maximum  to  which  the 
bridge  will  be  subjected. 

Importance  of  traffic,  and  the  hardship  which  might  result  thereto  from  temporary 
disablement  of  the  structure. 

Probability  of  early  renewal  on  account  of  change  of  line,  etc.  A  higher  limit 
might  be  allowed  for  a  short  time  to  meet  an  emergency  than  would  be  proper  for  a 
structure  to  be  kept  in  service  indefinitely. 

General  reliability  of  the  data  upon  which  the  investigation  of  the  structure  is 
based. 

Generally,  judgment  founded  upon  all  of  the  factors  surrounding  the  bridge,  its 
location,  service,  and  condition. 

It  must  be  recognized  that  there  is  danger  in  setting  down  a  hard-and-fast  rule  for 
the  limits  to  which  structures  might  be  stressed.  In  all  cases  it  is  necessary  to  exercise 
care,  knowledge,  and  good  judgment,  in  order  to  be  always  on  the  safe  side  and  at  the 
same  time  conserve  the  maximum  life  of  the  structure. 


Standard  Loadings 

In  the  systematic  investigation  of  a  large  number  of  bridges,  it  is  necessary  to  have 
a  unit  loading  as  a  basis  of  comparison.  The  familiar  Cooper's  Series  of  Standard  Train 
Loadings  furnishes  a  convenient  and  well-known  basis.  This  series  consists  of  two 
consohdation-type  engines,  followed  by  a  train  load  having  a  fixed  spacing  of  wheels 
and  a  fixed  relation  between  the  weights  on  the  various  wheels.  These  weights,  however, 
are  directly  proportionable  to  the  classes;  i.e.,  the  drivers  for  Class  E-40  Loading  have 
40,000  lbs.  on  each  axle;  for  Class  E-50  Loading,  50,000  lbs.  on  each  axle;  etc.  The 
imit  loading  in  this  Series  is  taken  as  Class  E-1  Loading. 

On  account  of  the  fixed  wheel  rearrangement  for  all  classes  and  the  proportion- 
ality of  wheel  loads,  it  follows  that  the  stresses  in  all  parts  of  bridges  due  to  these  loadings 
are  directly  proportionable  to  the  classes;  that  is,  the  stresses  in  every  part  of  the 
structure  from  Class  E-50  Loading  will  be  just  fifty  times  the  stresses  from  Class  E-1 
Loading, 


412  ECONOMICS    OF   BRIDGEWORK  Chapter  XLI 

In  connection  with  the  Hve-load,  it  is  necessary  to  make  proper  allowance  for 
"impact,"  "centrifugal  force,"  and  "traction."  The  general  method  of  investigating 
any  part  of  a  bridge  and  of  making  a  classification  is  as  f oUows ; 

1.  The  maximum  allowable  stress  is  determined,  which,  in  the  simpler  cases,  is 

the  cross-sectional  area  of  ttie  member  multiplied  by  the  limiting  unit  stress 
allowed. 

2.  Deduct  from  this  the  total  amoimt  of  stress  in  the  part  due  to  both  "Dead 

Load"  and  "Wind  Load."     The  remainder  gives  the  allowable  stress  for 
the  "Live  Load"  effect. 

3.  Dividing  this  by  the  stress  for  unit  "Live  Load"  (Class  E-1)  gives  the  classi- 

fication for  allowed  "  Live  Load,"  if  at  rest. 

4.  Divide  this  classification  by  the  term  which  takes   into  account  the   extra 

effects  of  the  "Live  Load,"  due  to  Impact  and  Centrifugal  Force,  and  the 
result  wiU  be  the  classification  of  the  allowed  "  Live  Load  "  at  fuU  speed. 

Classification  of  Loadings 

The  "Class  E"  loading  above  described  is  an  assumed  typical  loading.  Actual 
engine  and  car  loadings  vary  a  great  deal  as  to  spacing  of  the  wheels  and  the  distribution 
of  the  weight  on  the  various  axles.  The  effects  of  different  loadings  on  bridges  are  not 
in  direct  proportion  to  the  weight  of  the  engine  or  cars,  but  depend  on  the  number  of 
wheels,  spacing  of  wheels,  distribution  of  weight,  etc.  Actual  engine  loadings  can, 
however,  be  reduced  to  equivalents  in  the  standard  train  loadings,  corresponding  to  the 
different  span  lengths. 

This  is  done  by  computing  the  maximum  bending  moments  and  end  shears  for  the 
given  train  loadings  for  each  different  span  length.  These  are  divided  by  the  maximum 
bending  moments  and  end  shears  for  the  Unit  Class  "E-1 "  loading,  for  the  corresponding 
span,  the  result  being  the  "Classification"  of  the  loading. 

As  an  illustration  of  classification  of  various  engine  loadings.  Fig.  41o  is  given. 
This  shows  the  classification  of  several  types  of  the  new  standard  locomotives  which 
have  been  purchased  by  the  Government  and  are  now  being  assigned  to  the  various 
railroads.     Fig.  41&  shows  similar  classifications  for  typical  car  loadings. 

In  placing  restrictions  on  the  use  of  car  loadings  over  bridges,  it  is  not  practicable 
to  take  into  account  all  of  the  variations  in  car  lengths  which  occur.  An  equivalent 
for  the  various  car  loadings  can  be  arrived  at  by  considering  typical  hopper  cars  about 
33  ft.  long,  as  shown  in  Fig.  416,  for  which  the  wheel  spacing  given  is  a  fair  average. 
For  bridges  under  50-ft.  span,  the  trucks  of  two  adjacent  cars  produce  the  maximum 
effects,  and,  for  like  axle  loads,  are  independent  of  the  lengths  of  the  cars. 

The  approximately  parallel  curves  on  the  diagram  represent  the  classification  of 
these  typical  car  loadings  for  different  weights  of  cars,  where  the  total  weight  repre- 
sents the  weight  of  the  car  and  contents.  The  said  diagram  shows  by  dotted  line  the 
classification  of  a  typical  ore-car  loading,  which,  on  account  of  the  extremely  short  length 
of  the  car,  produces  a  high  classification  on  the  long  sjians;  and  it  records  also  the 
classification  of  a  heavy  wrecking  crane  of  120  tons  capacity. 

Speed  Restrictions 

In  the  foregoing  the  classification  has  been  determined  with  an  allowance  for  the 
effect  of  the  maximum  speed  over  bridges. 

Where  speed  is  reduced,  the  effects  of  the  live  k)ad  are  much  less;  and  the  allow- 
ance for  impact  and  centrifugal  force,  if  any,  may  be  correspondingly  reduced.  This 
will,  of  cour.se,  permit  heavier  loadings  to  be  oiierated  at  reduced  speed  as  compared 
with  those  permissible  for  full  speed. 


ECONOMICS   OF   MAINTENANCE   AND   REPAIRS  413 

10     20      30     40      50      60     70      80_90      100     110     110     130     140    150 

f65 


10     ZO     30     40      30      60      70     80     90     100     110     llO     IdO     140    150 

Spon  in  Feef 
Fig.  41a.     Diagram  Showing  Classification  of  U.  S.  Government,  Standard  Locomotives. 


%^.5iiMtw^^}sr-i'fxks 


•S3C. 


u. 


'/4&::: 


$■6 


;lt 


31 


IS 


■5P?5 


T^.--  ZZ-ff  t 


ii 


^Wti's 


20  40  60         80         100         JZO         140         160 

Span  Jo  Feef 

Fig.  416.    Diagram  Showing  Classification  of  Typical  Loadings 


180       200 


414  ECONOMICS   OF   BRIDGEWORK  Chapter  XLI 

From  the  tests  conducted  by  the  American  Railway  Engineering  Association,  it  is 
found  that  the  maximum  impact  which  will  be  obtained  at  reduced  speed  is : 

Less  than  30%  for  speed  of  10  miles  per  hour. 

Less  than  40%  for  speed  of  15  miles  per  hour. 

Less  than  50%  for  speed  of  20  miles  per  hour. 

Less  than  55%  for  speed  of  25  miles  per  hour. 

An  inspection  of  the  diagrams  indicates  that  the  effective  span  of  the  bridges  and 
the  characteristics  of  the  engine  loadings  determine  to  a  great  extent  whether  a  given 
loading  can  be  run  over  the  bridge,  and  shows  that  it  is  unsafe  to  attempt  to  decide 
whether  any  engine  loading  can  be  handled  over  a  structure  simply  by  knowing  its  total 
weight. 

There  is,  unfortunately,  a  misunderstanding,  among  some  railroad  operating 
officials,  as  to  the  effect  on  bridge  structures  of  such  complex  loadings  as  locomotives 
and  cars.  In  these  cases  it  is  assumed  that  the  effect  is  the  same  for  all  locomotives  of 
the  same  total  weight;  and  bridges  are  classified  as  being  safe,  or  otherwise,  for  all 
locomotives  of  given  total  weights.  If  this  practice  must  be  resorted  to,  the  limits 
set  should  be  on  a  very  conservative  basis ;  for  otherwise  there  would  be  danger  of  certain 
types  of  locomotives  having  a  serious  effect  on  some  bridges,  producing  unsafe  condi- 
tions. The  practice  would  not  be  economical,  because  it  would  either  lead  to  the 
premature  renewal  of  some  bridges  or  to  an  unnecessary  ruling  off  of  certain  types  of 
engines. 

Where  Low  Classification  Usually  Occurs  in  Bridges 

In  older  bridges  there  are  certain  parts  where  low  classifications  can  usually  be 
expected.  These  have  been  found  to  occur  most  often  in  the  lightest  members  of  the 
structure  and  in  members  which  carry  the  smallest  dead-load  stresses.  In  propor- 
tioning a  member,  a  part  of  the  sectional  area  thereof  can  be  taken  as  carrying  dead- 
load  stress  and  the  remainder  live-load  stress.  As  the  dead-load  stress  is  constant,  a 
smaller  area  would  be  required  where  a  higher  unit  stress  is  used.  This,  therefore, 
leaves  a  portion  of  the  area  originally  provided  for  dead-load  stress  available  to  carry 
live-load  stress. 

It  .is  found  that  the  floor  systems  of  bridges  have  generally  a  lower  classification 
than  the  girders  or  chords  of  the  trusses.  The  low  classification  of  stringers  is  generally 
in  the  section  of  the  flanges  near  the  center,  in  the  riveting  of  flanges  near  the  ends  (par- 
ticularly if  they  are  shallow),  and  in  the  riveting  connecting  the  stringers  to  the  floor 
beams. 

Floor  beams,  if  of  shallow  depth,  frequently  show  a  low  classification  in  flanges 
near  the  stringer  connections,  also  in  the  riveting  of  flanges  near  the  ends,  and  in  splices 
connecting  the  wtbs  of  the  floor  beams  to  the  gusset  plates,  particularly  in  types  where 
the  lower  part  of  the  floor  beam  is  cut  out  to  fit  around  the  ends  of  the  trusses  or  over 
pins. 

In  plate  girders,  the  flanges  frequently  show  low  classification  at  points  whei-e  the 
web  is  not  fully  spliced  near  the  center  and  at  points  near  the  ends  of  cover  i)lates. 
The  flange  riveting  near  the  ends  of  girders  frequently  has  a  k)w  classification,  par- 
ticularly where  the  girders  are  shallower  at  the  ends. 

Webs  of  plate  girders  show  low  classification  near  the  ends  of  the  girders  where 
there  is  a  relatively  large  expanse  of  web,  unsupported  by  stiffeners.  The  web  splices 
near  the  ends  of  the  span  have  a  low  classification  where  only  one  line  of  rivets  is  used 
on  each  side  of  the  splice. 

In  trusses,  the  i)osts  and  diagonals  near  the  center  of  the  span  usually  show  a  low 
classification.  This  is  particularly  true  of  the  diagonals  and  counter-diagonals  of  light 
eye-bars  or  loop  rods. 

Suspenders,  or  hip-vertical  members,  frequently  have   a  low  classification.     The 


ECONOMICS   OF  MAINTENANCE   AND   REPAIRS  415 

classification  of  end  posts  and  top  chords  of  truss  bridges  is  frequently  low  on  account 

of  the  eccentricity  of  the  member  with  respect  to  the  location  of  the  pin. 

The  pins  of  old  truss  bridges  frequently  show  a  startUngly  low  classification  where 
computations  are  made  in  accordance  with  the  usual  methods;  hence  it  is  necessary  to 
take  advantage  of  certain  conditions  which  are  more  favorable  than  the  usual  assump- 
tion, in  order  to  help  out  the  classification.  Where  eye-bar  members  consisting  of  more 
than  two  pairs  of  eye-bars  meet  on  a  pin,  a  slight  redistribution  of  stress  in  the  several 
eye-bars  wiU  frequently  increase  the  classification  of  the  pin;  and  this  is  justifiable  as 
being  in  line  with  the  way  the  structure  actually  works.  Where  certain  members  have 
wide  bearing  surfaces  on  the  pins,  the  center  of  pressure  can  be  taken  near  one  edge  of 
the  bearing  surface,  thus  increasing  the  classification  of  the  pin  and,  at  the  same  time, 
approximating  more  nearly  to  the  actual  behavior  of  the  detail.  It  is  also  permissible 
to  use  higher  unit  stress  for  figuring  pins  than  for  the  other  members  of  the  structure. 
The  following  illustrates  what  might  be  considered  permissible,  providing  there  is 
assurance  that  the  material  is  of  good  quality  and  that  the  computations  take  account 
of  all  the  forces  acting: 

Wrought  iron 40,000  lbs.  per  sq,  in.  in  bending 

Softsteel  (.1%C) 45,000    "    "        " 

Structural  steel   (.2 %C) 48,000    "    "        "  *♦ 

Mild  "    (.25%C) 52,000    "    "        **  tt 

Medium         "    (.35%C) 56,000    "    "        «*  tt 

Hard  "    (.45%C) 64,000   "    "       *t         ti 

It  is  to  be  noted  that,  In  bridges  built  in  the  late  80's  and  early  90's,  hard  grades  of  steel 
were  frequently  used  for  the  pins. 

In  timber-trestle  bridges,  the  stringers  in  bending  usually  show  low  classification. 
On  account  of  there  being  three  or  more  sticks  acting  together,  it  is  permissible  to  use  a 
higher  unit  stress  for  trestle  stringers  than  for  a  single  stick,  as  the  average  strength 
for  the  several  pieces  exceeds  that  of  the  poorest  one.  On  account  of  the  exposure 
to  the  weather  and  the  deterioration  which  gradually  takes  place,  the  allowed  xmit 
stress  in  timber  stringers  should  be  reduced  as  the  age  of  the  bridge  increases.  Where 
timber  bridges  are  thoroughly  inspected  and  defective  material  is  promptly  replaced, 
and  where  they  are  subject  to  the  same  general  consideration  as  given  above  for  metal 
bridges,  the  following  unit  stresses  might  be  taken  as  a  safe  practice  for  maximum  fiber 
stress  in  stringer  bridges  without  allowance  for  impact: 

For  stringer  bridges  six  years  old,  2,000  lbs.  per  sq.  in.,  and  reduced  about  100  lbs. 
per  sq.  in.  for  each  year  following. 

The  above  figures  are  based  on  Douglas  Fir  or  dense  yellow  pine  and  for  climatic 
conditions  prevailing  in  the  North  Central  States.  In  more  arid  regions  where  longer 
life  of  timber  may  be  expected,  the  reduction  in  stress  for  age  need  not  be  so  rapid. 
On  account  of  the  comparatively  short  life  of  timber  bridges  and  the  ease  with  which 
they  can  be  renewed,  there  is  not  generally  the  same  urgency  in  establishing  maximum- 
safe-stress  limits  as  in  the  case  of  the  more  permanent  metal  bridges.  In  timber  truss- 
bridges  the  lowest  classification  usually  occurs  in  the  floor  beams,  truss  rods,  and  diag- 
onal braces. 

It  has  been  foimd  that  metal  bridges  suffer  frequently  from  corrosion  in  the  top 
flanges  of  stringers  and  floor  beams,  on  account  of  the  action  of  brine  drippings  from 
refrigerator  cars. 

In  bridges  where  the  ties  are  supported  on  shelf-angles  riveted  to  the  webs  of  the 
girders,  the  shelf-angles  frequently  show  considerable  corrosion  and  tend  to  break  in 
the  root  of  the  angle. 

In  pin-connected  trusses,  excessive  wear  sometimes  takes  place  in  the  pin  bearings, 
particularly  in  draw  bridges. 


416  ECONOMICS  OF  BRIDGE  WORK  Chapter  XLI 

Metal  bridges  and  viaducts  over  railroad  tracks  frequently  show  excessive  corrosion 
in  the  floor  system  and  laterals,  due  to  smoke  and  gas  from  locomotives,  also  because  of 
the  fact  that  the  sohd  floors  of  such  bridges  do  not  permit  the  steel  work  beneath  to 
dry  out  quickly. 

MetaUic  overhead  bridges  having  a  scant  clearance,  so  that  the  stacks  of  the  loco- 
motives come  close  to  the  steelwork,  frequently  show  excessive  wear  from  the  sand- 
blasting effect  of  cinders  issuing  from  the  engine  exhaust,  particularly  when  the  loca- 
tion is  on  an  ascending  grade  where  the  locomotive  is  worked  hard  under  the  bridge. 

Possible  deterioration  of  the  structure  of  the  metal  itseh,  by  fatigue,  has  in  some 
quarters  been  a  matter  of  apprehension ;  but  it  now  seems  to  be  recognized  that  no  such 
interna]  deteriorating  action  takes  place  where  the  bridge  has  not  been  subjected  to 
excessively  high  stress.  If  crystallization  is  found  in  the  metal  of  a  structure,  it  prob- 
ably was  there  at  the  time  the  structure  was  built,  and  is  due  to  improper  methods  of 
manufacture  of  the  material. 

It  may,  therefore,  be  taken  as  a  certainty  that  iron  and  steel  bridges,  if  not  reduced 
in  section  by  rust,  etc.,  and  if  not  shaky  on  account  of  inadequate  bracing,  are  fuUy 
capable  of  carrying  the  figured  loads  at  reasonable  limiting  unit  stresses,  provided  they 
are  carcfuUy  inspected  and  properly  maintained. 

Strengthening  of  Light  BniDGEa 

Strengthening  of  light  bridges  may  be  either  a  matter  of  reinforcing  minor  details 
which  are  found  to  hmit  the  carrying  capacity  of  the  structures,  or  may  consist  of  heavy 
reinforcing  in  an  attempt  to  increase  the  strength  thereof  throughout.  The  minor 
strengthening  can  usually  be  done  at  small  expense;  and  it  is  an  economical  method  of 
getting  considerably  greater  life  out  of  bridges.  Heavy  reinforcing  may  or  may  not  be 
an  economical  proposition,  as  it  involves  work  being  done  in  the  field,  which  is  costly, 
and  the  maintenance  of  traffic  during  the  time  the  work  is  in  progress,  which  involves 
some  risk  to  traffic  and  is  usuafly  expensive.  On  very  large  bridges  where  the  cost  of 
replacing  is  great,  some  extensive  strengthening  operations  have  been  carried  out 
economically. 

In  making  plans  for  reinforcing  bridges,  it  is  usually  preferable  to  add  new  material 
to  the  structure  so  that  the  present  structure  is  not  temporarily  weakened,  rather  than 
to  remove  parts  and  substitute  heavier  ones,  though  the  latter  expedient  has  some- 
times to  be  resorted  to.  The  descriptions  of  the  points  at  which  low  classification  usually 
occurs  suggest  in  themselves  how  these  might  be  strengthened. 

In  plate  girders  the  top  and  bottom  flanges  may  be  reinforced  by  additional  cover 
plates,  particularly  at  points  where  the  web  is  spliced  and  not  effective  for  carrying 
its  proportion  of  the  bending  stress.  Where  there  are  no  cover  plates  on  the  girders, 
cover  plates  of  desired  length  can  be  added.  On  plate  girders  where  there  are  two  or 
more  cover  plates,  additional  cover  plates  would  be  nearly  the  full  length  of  the  girder 
and  expensive  to  apply.  Plate  girders  can  be  doubled  up  to  make  deck  si)ans,  using 
three  or  more  girders  per  span  at  small  expense,  thereby  using  up  light  girders  and  jiro- 
viding  bridges  of  large  carrying  capacity. 

Where  waterways  or  other  under-crossing  conditions  permit,  timber  bents  can  be 
placed  under  spans  to  strengthen  them. 

Where  the  rivets  in  the  flanges  of  girders  show  low  classification,  larger  rivets  can  be 
substituted  for  existing  rivets,  or,  where  the  rivet  spacing  permits,  additional  rivets 
can  be  driven. 

Where  the  web  plates  give  a  low  classification,  additional  stiffeners  can  be  placed 
in  the  panels  near  the  ends  of  the  girders  to  provide  extra  support  for  the  web  and 
thereby  increase  its  classification. 

Sh(^lf-anf!;l('s  can  bo  strengthened  by  placing  short  vertical  stiffeners  beneath  them. 
Where  web  splices  with  low  classific^ation  o(!cur,  these  can  be  replaced  with  wider  splice 
plates  having  additional  rows  of  rivets  in  the  splice. 


ECONOMICS   OF  MAINTENANCE   AND   REPAIRS  4l7 

In  through  bridges  the  stringers  can  be  reinforced  by  additional  riveting,  by  the 
placing  of  additional  stringers,  either  timber  or  steel,  and  by  shifting  existing  stringers 
to  secure  better  distribution  of  the  load.  Where  str;':>ger3  are  spaced  so  that  some  of 
them  do  not  carry  their  full  proportion  of  load,  it  is  possible  to  introduce  cross  bracing 
so  that  all  the  stringers  in  the  panel  shall  act  together  to  carry  the  total  load  and  thus 
relieve  the  excessive  burden  on  certain  stringers. 

Floor  beams  can  be  reinforced  by  cover  plates  or  angles  added  to  the  flanges,  by 
additional  riveting,  or  by  shifting  the  stringers  toward  the  trusses  so  as  to  reduce  the 
bending  in  the  beams. 

In  very  old  bridges  the  floor  beams  are  frequently  of  much  lower  classification 
than  the  remainder  of  the  bridge;  and  they  can  sometimes  be  replaced  with  entirely 
new  beams  at  a  reasonable  expense  so  as  to  get  additional  life  out  of  the  rest  of  the 
structure. 

In  trusses,  diagonals  and  counters  can  usually  be  reinforced  with  additional  bars 
or  rods  having  loops  over  the  truss  pins  and  being  connected  by  turn-buckles  to  provide 
adjustment.  Similarly,  bottom  chords  of  eye-bars  can  be  reinforced  with  additional 
bars  having  yokes  bearing  on  the  heads  of  the  original  eye-bars. 

End  posts  of  through  bridges,  whose  low  classification  is  due  to  eccentricity  of 
members,  can  be  strengthened  by  placing  angles  or  plates  on  the  sides  of  the  said  mem- 
bers, so  as  to  make  the  cross-sections  better  balanced,  thus  reducing  eccentricity. 

The  bottom  chords  of  truss  spans  may  be  reinforced  by  adding  an  auxiliary  bottom 
chord  above  the  present  chord  and  sloping  the  end  panels  to  meet  as  nearly  concentric 
with  the  end  pins  as  conditions  will  permit.  Auxiliary  web  members  may  be  con- 
nected to  the  new  auxiliary  bottom  chord  and  the  top  chord.  This  is  the  method 
employed  on  the  North  Halsted  Street  Viaduct  over  the  C.  M.  &  St.  P.  Ry.  Co.'s  tracks 
in  Chicago.  This  method  has  also  been  employed  by  the  City  of  Chicago  on  several 
bridges  in  that  city. 

Where  pins  have  low  classification,  it  is  sometimes  possible  to  move  the  members 
on  the  pin  and  reduce  the  bending.  In  some  cases,  diaphragms  placed  in  built-up 
members  will  reUeve  the  bending  on  the  pins.  The  pins  themselves  can  be  strengthened 
by  replacing  them  with  high-carbon  or  special-alloy  steel  pins  of  the  same  size;  or,  if 
still  more  strength  is  required,  by  boring  out  the  pin  holes  and  putting  in  larger  pins. 
This  operation  has  been  done  a  number  of  times;  but  it  requires  rather  elaborate  arrange- 
ments for  holding  the  members  in  position  while  the  pins  are  removed. 

Timber  truss-bridges  can  be  strengthened  by  placmg  floor  beams,  diagonal  braces, 
or  truss  rods  where  needed. 

Where  timber  trusses  are  old  and  have  commenced  to  open  slightly  in  the  joints 
or  to  show  other  signs  of  diminished  strength,  they  can  be  temporarily  strengthened 
and  carried  for  a  few  more  years  by  placing  timber  bents  under  the  panels  points  at 
two  or  three  panels  from  the  end  of  the  span.  This  has  the  effect  of  reducing  the  span- 
length  and  stiffening  the  structure. 

Timber-trestle  bridges  can  be  readily  strengthened  by  additional  stringers. 

The  cost  of  strengthening  bridges  varies  with  the  size  of  the  job,  the  amount  of 
staging  required,  the  amount  of  moving  the  same  about  so  as  to  reach  different  portions 
of  the  work,  the  size  of  the  crew  available,  the  distance  traveled  by  the  crew,  the  tools  at 
hand,  etc.  In  a  general  way,  it  has  been  found  that  the  cutting  out  and  replacing  of 
rivets  on  ordinary  strengthening  jobs  costs  from  25c.  to  75c.  each.  DriUing  new  holes 
and  driving  new  rivets  therein  cost  from  50c.  to  $1.00  each;  i.e.,  the  cost  of  such  work 
will  be  given  by  the  total  number  of  rivets  driven  at  these  imit  prices,  plus  the  cost  of  the 
additional  material  required. 

With  the  maintenance  of  old  and  hght-capacity  bridges,  the  question  continually 
arises  whether  it  is  more  economical  to  strengthen  the  structure  or  to  renew  it.  As  a 
general  proposition,  it  would  be  permissible  to  spend  each  year  for  strengthening  an 
amount  equal  to  the  interest  on  the  investment  in  a  new  bridge,  less  the  cost  of  addi- 


418 


ECONOMICS   OF   BRIDGEWORK 


Chapter  XLI 


tional  maintenance  required  by  the  old  bridge  on  account  of  the  greater  attention  it 
receives. 

For  illustration,  let  us  consider  a  few  lengths  of  through  spans  designed  for  E-55 
loading,  replacing  similar  spans  designed  in  the  early  90's.  New  steel  work  taken 
at  5c.  per  pound  erected;  falsework  at  $10.00  per  lineal  foot;  removing  old  structure 
at  $10.00  per  ton;  salvage  on  old  spans  at  22-c.  per  pound;  additional  cost  of  main- 
tenance of  the  old  span  on  account  of  additional  inspection,  classification,  and  super- 
vision required,  $1.00  per  foot  of  span  per  year.  The  last  column  of  the  following 
table  shows  the  amount  which  we  could  afford  to  spend  per  year  in  strengthening  old 
spans  rather  than  to  renew  them.  The  costs  shown  in  this  table  are  for  illustration 
only.  As  they  fluctuate  from  time  to  time,  the  resulting  economics  will  vary  accord- 
ingly: 

TABLE   41a 


Available 

Interest  on 

for 

Span 

New  Steel 
Weight 

Cost 
Erected 

Salvage 

Net 

Net  Cost 
at  5% 

Strengthen- 
ing Each 
Year 

50' 

66,000  lbs. 

$  4,330 

$  1,130 

$  3,200 

$    160 

$    110 

100' 

218,000 

13,390 

3,700 

9,690 

485 

385 

200' 

800,000 

46,000 

12,500 

34,500 

1,725 

1,525 

300' 

1,600,000 

92,200 

25,000 

67,200 

3,360 

3,060 

The  writer  has  in  mind  a  bridge  having  three  400  ft.  spans  which,  if  renewed  about 
ten  years  ago,  as  some  Railroad  Managements  might  have  done,  would  have  cost  about 
$370,000  after  deducting  the  salvage  value  of  old  spans  recovered.  The  interest  on 
this  investment  for  the  ten  years  would  have  amounted  to  about  $185,000.  Instead, 
however,  of  replacing  these  spans,  they  have  been  carefully  maintained  and  inspected 
and  the  details  strengthened  wherever  the  classification  showed  that  it  was  necessary 
to  carry  the  heavier  traffic.  The  actual  cost  of  strengthening,  together  with  the  addi- 
tional maintenance  expense,  has  amounted  to  not  over  $20,000  during  tliis  period, 
showing  a  saving  for  this  bridge  of  about  $165,000;  because  of  the  policy  of  getting  the 
longest  practicable  life  out  of  structures. 

This  illustration  is  intended  to  show  only  one  way  in  which  the  problem  may  be 
considered.  With  old  and  light  bridges  a  limit  is  reached  beyond  which  it  is  not  econom- 
ical to  strengthen  them ;  and  replacement  then  becomes  necessary.  It  must  be  recog- 
nized, of  course,  that  a  newly  designed  and  heavy  structure  is  preferable  to  a  lighter 
one.  It  is  possibly  true  that,  in  case  of  a  serious  derailment  on  a  bridge,  a  light  structure 
might  be  destroyed  while  a  heavy  new  structure  might  withstand  the  same  treatment 
without  being  seriously  disabled.  Such  considerations  must  be  taken  into  account  in 
shaping  the  general  policy  concerning  the  keeping  of  light  bridges  in  service. 


From  tho  data  furnished  by  Mr.  Heritage,  tlic  following  has  been 
excer[)ted : 

Strictly  speaking,  the  economics  of  nia.iiitonaiu'o  iiud  r(^pairs  starts  with 
the  design  of  the  bridge.  The  most  (H'ononiical  structure  is  that  on  which 
the  total  fixed  annual  charges  are  a  mininmni — these  charges  to  include 


ECONOMICS   OF   MAINTENANCE   AND   REPAIRS  419 

interest  on  the  original  investment,  annuity  to  provide  for  the  replacement 
of  the  structure  when  the  time  comes  for  its  renewal,  insurance  when  neces- 
sary, and  charges  for  maintenance  and  repairs. 

It  is  evident  that,  by  increasing  the  original  investment,  we  can  usually 
provide  a  structure  that  will  have  a  longer  life  and  will  require  less  annual 
expenditure  for  maintenance  and  repairs.  However,  we  are  considering 
here  only  the  subject  of  maintenance  and  repairs,  and  shall  take  into 
account  only  such  structures  as  are  actually  built,  the  economics  of  design 
and  the  types  of  structure  best  suited  for  various  purposes  and  conditions 
having  been  covered  in  other  chapters. 

All  structures  should  have  periodical  and  careful  inspection;  and  when 
anything  is  found  requiring  attention,  it  should  be  done  promptly.  The 
neglect  of  attending  quickly  to  minor  repairs  needed  will  usually  result  in 
much  more  extensive  and  costly  repairs  later  on;  for,  according  to  an  old 
and  well  known  proverb,  "a  stitch  in  time  saves  nine." 

When  an  organization,  such  as  a  Railway  Company  or  a  City,  has  a 
large  number  of  bridges  to  maintain,  it  is  customary  to  have  a  department 
to  look  after  the  work,  with  the  requisite  force  of  men  and  the  necessary 
equipment;  and  these  should  be  continually  engaged  in  making  repairs  to 
bridges  and  like  structures. 

Repairs  to  timber  bridges  are  more  frequent  than  those  on  permanent 
structures,  on  account  of  the  liability  of  timber  to  decay.  Wood  preserva- 
tion, especially  by  the  process  of  creosoting,  has  taken  wonderful  strides  in 
the  last  few  years.  With  the  growing  scarcity  of  timber  and  the  rise  in 
its  price,  such  preservation  will  increase  until  it  will  be  the  exception  rather 
than  the  rule  to  have  untreated  timbers  in  exposed  structures.  The 
majority  of  wooden  bridges  now  in  service  on  railways  are  trestles;  although, 
in  some  parts  of  the  country,  timber  or  combination-timber-and-steel  truss- 
spans  are  still  used.  Timber  structures  can  be  kept  up  almost  indefinitely 
by  replacing  members  shortly  before  they  become  dangerously  decayed; 
however,  when  a  bridge  is  so  old  that  a  large  portion  of  the  timber  shows 
more  or  less  decay,  it  is  more  economical  to  renew  the  whole  structure, 
salvaging  such  second-hand  material  as  possible,  after  which  the  bridge 
will  be  serviceable  without  further  repairs  for  a  period  of  years. 

In  case  of  pile-driven  trestles,  it  is  cheaper  under  some  conditions  to 
replace  the  piles  with  frame  bents  than  it  would  be  to  renew  the  structure 
as  a  pile-driven  trestle.  In  this  case  the  old  piles  are  cut  off  under  the 
ground  until  sound  timber  is  reached,  usually  about  two  or  three  feet;  and 
the  new  frame  bents  are  supported  on  these  old  piles.  The  latter  usually 
rot  off  close  to  the  ground  line;  but  in  good  soil  they  will  remain  sound  at  a 
depth  of  two  or  three  feet  for  a  long  period  of  years.  The  objections  to 
this  procedure  are  that  the  sill,  being  underground,  is  difficult  to  inspect 
and  that  a  frame  bent  structure  is  not  as  stiff  as  a  pile  structure;  conse- 
quently, if  a  pile  driver  is  available,  it  is  preferable  to  drive  pile  bents  rather 
than  to  construct  frame  ones. 


420  ECONOMICS   OF  BKIDGEWORK  Chapter  XLI 

In  making  repairs  and  renewals  to  timber  bridges — and,  in  fact,  all 
bridges — the  bridge  gangs  formerly  were  usually  equipped  with  only  hand 
tools;  but,  now  that  the  cost  of  labor  is  so  much  greater,  it  is  economical  to 
replace  manual  labor  as  far  as  possible  with  machines.  A  hght^derrick 
car  equipped  with  a  hoisting  engine  or  a  locomotive  crane  will  save  the 
work  of  many  men  in  handling  heavy  bridge  material.  On  timber  struc- 
tures a  large  part  of  the  labor  consists  of  boring  holes  for  bolts  and  fasten- 
ings. Repair  gangs  should  be  equipped  with  boring  machines  operated 
by  either  air  or  electricity,  in  order  to  do  this  work  economically.  The 
magnitude  of  the  task  will  determine  whether  machinery  or  hand  labor  is 
the  more  economical.  On  very  small  jobs  it  will  be  more  costly  to  set  up 
the  equipment  than  it  would  be  to  do  the  work  with  hand  tools;  however, 
the  tendency  is  to  make  more  and  more  use  of  machines  instead  of  manual 
labor. 

The  preservation  of  timber,  in  order  to  increase  its  hfe  and  reduce  the 
necessary  maintenance,  has  been  mentioned.  Formerly  timber  highway 
bridges  were  commonly  covered  by  roofs  and  siding  to  protect  the  frame 
work  from  the  weather;  and  such  structures  lasted  for  a  long  period  of 
years,  several  notable  wooden  bridges  in  this  country  having  reached  an 
age  of  nearly  100  years.  This  sort  of  bridge  accumulated  a  great  deal  of 
dirt  and  was  very  dark  at  night,  and  the  roof,  housing,  and  floor  naturally 
required  considerable  maintenance. 

The  question  of  fire  protection  should  also  receive  proper  attention  in 
connection  with  timber  bridges.  The  expense  caused  by  a  burned  bridge 
in  some  cases  far  exceeds  the  value  of  the  structure  itself,  as,  for  instance, 
on  a  railway  where  the  traffic  is  stopped  on  this  account.  On  railways, 
timber  trestles  are  frequently  partially  protected  from  fire  by  covering  the 
deck  with  sheet  metal  or  with  stone  or  gravel,  so  that  sparks  from  a  defec- 
tive engine  will  not  set  it  ablaze.  Sometimes  fire-proof  paints  are  used. 
Some  of  these  paints  are  very  effective  for  several  years,  and  at  the  same 
time  are  good  timber  preservers;  hence,  if  properly  selected,  they  will  be 
economical  from  a  maintenance  standpoint  as  well  as  in  respect  to  protec- 
tion from  lire.  The  timber  floors  on  highway  bridges  and  the  ties  on  rail- 
way bridges  are  subject  to  wear,  and  are  usually  worn  out  before  they  rot 
out;  In  cases  of  very  heavy  traffic,  bridge  floors  should  be  constructed  of 
more  permanent  material  than  planks;  and  the  ties  on  railroad  bridges 
should  be  protected  with  tic  plates. 

Old  stone  piers  and  abutments  often  show  open  seams  where  the  mortar 
has  fallen  out  of  the  joints.  If  these  receive  attention  in  time,  it  will  usually 
be  sufficient  to  dig  the  old  mortar  out  of  the  seams  and  repoint  them,  thus 
protecting  the  interior  of  the  structure  from  moisture;  but  in  some  cases 
more  work  than  that  is  necessary.  On  high  structures,  especially  over 
rivers,  it  is  very  costly  to  put, the  spans  on  falsework  in  order  to  repair  or 
rebuild  pi(!rs,  hence  other  expedients  arc  resorted  to,  in  order  to  avoid  this 


ECONOMICS   OF   MAINTENANCE   AND   REPAIRS  421 

expense.  Sometimes  a  jacket  of  reinforced-concrete  can  be  built  around  an 
old  pier  and  the  top  protected  with  a  water-proof  coating. 

Concrete  has  largely  displaced  stonework  for  the  material  of  sub- 
structures in  bridges.  Piers  made  of  iron  or  steel  cylinders  and  filled  with 
concrete  provide  a  cheap  construction  where  conditions  are  suitable.  They 
were  formerly  largely  used  for  railroad  bridges,  but  their  employment  is 
now  confined  mostly  to  a  light  class  of  highway  bridges  or  to  railroad 
bridges  carrying  only  light  loading.  If  this  type  of  pier  is  very  high,  it  is 
subject  to  vibration  under  traffic;  and  this  vibration  will  produce  an 
injurious  effect  on  the  superstructure  as  well  as  on  the  piers.  Many  piers 
of  this  class  are  kept  in  service  by  encasing  them  in  concrete,  thus  increas- 
ing their  weight  and  stability ;  and  this  can  usually  be  done  without  putting 
the  bridge  on  falsework  and  removing  the  old  piers,  because  the  spans  will 
be  supported  upon  the  old  cylinders  while  the  new  work  is  in  progress. 

Steel-frame  structures  are  subject  to  deterioration  by  corrosion;  and 
to  prevent  this  the  surface  must  be  always  covered  by  a  protective  coating, 
usually  paint.  Since  corrosion  will  gradually  eat  away  metal  which  cannot 
be  replaced,  it  is  evident  that  this  protection  is  of  the  utmost  importance. 
In  many  cases  it  does  not  receive  the  attention  it  deserves.  Many  bridges 
have  been  seriously  damaged  by  rust,  even  to  the  extent  of  having  to  replace 
them,  all  of  which  expense  could  have  been  prevented  by  keeping  the 
structures  properly  painted.  Railroads  usually  recognize  the  importance 
of  painting,  and  seldom  allow  the  rust  to  accumulate  to  the  extent  of  weak 
ening  the  structure.  However,  even  on  railroads,  bridges  are  found  thai 
have  been  materially  damaged  by  corrosion.  There  are  parts  speciallj 
subject  to  rust,  such  as  the  top  flanges  of  deck  girders  and  of  stringers  thai 
are  more  or  less  hidden  by  the  ties,  and  which  sometimes  become  badly 
corroded  while  the  paint  on  the  main  body  of  the  structure  is  still  in  a  good 
state  of  preservation.  Also  parts  of  highway  bridges  underneath  the  floor 
are  frequently  in  bad  condition,  owing  to  the  fact  that  they  cannot  be 
noticed  by  anyone  crossing  the  bridge.  However,  if  proper  provision  for 
inspection  at  regular  intervals  is  made,  there  is  no  excuse  for  this  condi- 
tion resulting  in  damage  to  the  structure. 

There  are  many  varieties  of  paint  recommended  for  steel  bridges. 
The  best  are  usually  the  most  expensive  but  will  be  the  most  economical  in 
the  end.  The  application  of  paint  being  about  twice  as  costly  as  the 
material,  a  saving  of  a  considerable  percentage  in  cost  of  paint  will  result 
in  only  a  small  percentage  of  economy  on  the  entire  job.  The  result  is 
that  the  cheaper  paints  will  last  probably  two  or  three  years  less  than  will 
the  more  expensive  ones.  The  subject  of  bridge  paints  is  highly  technical 
and  cannot  be  gone  into  in  detail  here;  however,  it  is  important  to  note 
that  different  paints  should  be  used  for  different  conditions.  For  instance, 
a  paint  that  would  give  satisfactory  results  in  a  dry  climate  would  not  be 
suited  for  a  structure  subject  to  acid  fumes  or  engine  blasts,  as  on  bridges 


422  ECONOMICS   OF   BRIDGEWOEK  Chapter  XLI 

that  are  over  railroad  tracks,  or  for  a  moist  climate,  especially  near  salt 
water.  Some  paints  are  a  good  protection  against  corrosion  but  do  not 
stand  the  weather,  while  others  have  exactly  the  opposite  properties. 
Therefore,  the  first  or  priming  coat  should  be  of  the  first-mentioned  variety 
and  the  finishing  coats  of  a  paint  that  is  not  readily  affected  by  exposure 
to  the  weather.  The  most  commonly  used  and  satisfactory  paint  for  the 
priming  coat  is  pure  red  lead  ground  in  linseed  oil.  Sometimes  linseed  oil 
alone  is  used  and  sometimes  paint  with  a  Portland  cement  base.  For  the 
finishing  coats,  graphite  paints,  graphite  and  silica  paints,  or  paints  of  other 
carbon  pigments,  such  as  lamp  black  with  oxide  of  iron,  or  oxide  of  iron 
paints  are  most  frequently  employed.  The  latter  are  not  suitable  for  the 
priming  coat,  owing  to  the  fact  that  these  pigments  promote  oxidation,  a 
condition  that  is  often  ignored  in  practical  work. 

As  to  the  appHcation  of  the  paint — this  must  be  well  done,  if  satisfactory 
results  are  expected.  Metal  should  never  be  painted  when  it  is  damp,  in 
freezing  weather,  or  over  rust.  In  repainting  old  structures  probably  the 
most  important  consideration  is  the  cleaning  of  the  metal.  Paint  apphed 
over  rusted  surfaces  will  not  be  durable.  Further,  there  is  likehhood  of 
corrosion  spreading  underneath  the  paint,  and  then  the  protection  will 
soon  break  down.  As  previously  noted,  some  parts  of  the  structure  are 
subject  to  faster  deterioration  of  the  paint  than  other  parts.  This  is  true 
of  the  tops  of  stringers,  floor  beams,  and  compression  chords,  and  of  flat 
surfaces  exposed  to  weather,  especially  surfaces  beneath  the  floor,  such  as 
lateral  plates,  battens, etc.,  which  give  lodging  to  cinders  and  other  materials 
that  will  hold  moisture.  For  this  reason  a  very  satisfactory  method  to  use 
in  painting  an  old  bridge,  where  the  paint  is  bad  on  certain  parts  and  fair  on 
others,  is  to  clean  thoroughly  the  metalwork  and  paint  over  the  parts 
where  it  is  exposed  with  a  coat  of  red  lead  or  some  other  good  priming  paint, 
and  then  give  the  whole  structure  a  good  finishing  coat. 

As  to  the  method  of  cleaning  rust  from  the  metal — this  is  done  by  cut- 
ting with  chisels  and  hammers  and  by  scrubbing  off  with  wire  brushes,  or 
with  a  sand  blast.  The  latter  method  is  most  effective;  however,  it  is 
expensive  and  is  not  recommended  unless  the  bridges  are  in  a  bad  state  of 
corrosion.  Also  it  must  be  used  with  a  great  deal  of  caution  so  that  in 
removing  the  rust  an  excessive  amount  of  the  surrounding  metal  will  not 
be  cut  away  at  the  same  time. 

To  obtain  satisfactory  results,  a  great  deal  of  care  must  be  taken  in  apply- 
ing the  paint;  it  should  be  brushed  out  thoroughly  on  the  metal.  Recently 
painting  by  air-spraying  machines  has  come  into  extensive  use,  but  the 
employment  of  these  machines  on  bi'idgework  is  not  connnon.  It  is 
doubtless  a  labor  saver  and,  if  properly  handknl,  is  not  very  wasteful  of 
paint.  The  manufacturers  of  these  devices  claim  that  the  work  they  do  is 
superior  to  hand  painting;  and,  when  skilfully  used,  it  is  certain  that  good 
results  can  be  obtained.  Howevei-,  for  durability,  it  is  ]irobable  that  such 
coatings  arc  not  as  good  as  paint  well  brushed  on  ])y  hand;  still  it  might  be 


ECONOMICS   OF   MAINTENANCE   AND   REPAIRS  423 

economical  to  use  spraying  machines  on  bridges,  if  the  labor  cost  saved  will 
more  than  offset  the  decreased  life  of  the  paint.  Painting  by  spraying 
machines  would  be  satisfactory  on  large  vertical  surfaces,  such  as  the  sides 
of  girders  and  beams  and  the  faces  of  large  posts  and  columns;  but  it  is  not 
recommended  for  lattice  work  and  other  small  parts,  on  account  of  the 
wasting  of  paint.  One  advantage  derived  from  the  use  of  these  machines 
is  the  application  of  paint  in  places  that  are  difficult  to  reach  with  a  brush. 
On  flat  surfaces  like  walls,  recent  experiments  indicate  that  the  air  spray 
will  decrease  the  labor  cost  by  more  than  one-half,  with  a  slight  increase  in 
amount  of  paint  used,  about  5%;  but  similar  data  for  bridgework  are  not 
available. 

Deterioration  of  steel  structures  due  to  wear  will  be  apparent  in  the 
loosening  of  rivets  and  in  the  increased  vibration  caused  by  cutting  in  pins 
and  other  parts.  When  loose  rivets  appear  in  the  structure,  they  should  be 
cut  out  and  replaced.  They  are  generally  most  frequent  in  lateral  bracing 
of  stringers  and  girders  and  where  single-angle  bottom-laterals  are  attached 
to  the  stringers.  Also  stringer  and  floor-beam  connections  are  likely  to 
develop  loose  rivets  when  the  structure  is  overloaded. 

In  old  and  heavy  bridges  the  pins  will  often  show  considerable  wear. 
This  is  an  expensive  matter  to  repair,  as  it  involves  putting  the  structure  on 
falsework  and  the  use  of  considerable  machinery  to  re-drill  the  holes.  If 
pins  are  replaced,  the  new  pins  should  be  slightly  larger  than  the  original 
ones.  This  class  of  repair  work  is  not  often  done,  because  a  bridge  in  this 
condition  is  usually  very  much  overloaded  and  should  be  replaced  with  a 
heavier  structure.  Another  location  for  wear  is  at  the  intersection  of  diag- 
onal bars  that  are  in  contact.  In  order  to  prevent  these  bars  from  cutting 
away,  a  buffer  should  be  placed  between  them  and  clamped  thereto. 

On  old  bridges  it  is  frequently  found  that  the  eye-bars  making  up  one 
member  are  not  pulling  evenly.  If  the  member  consists  of  two  bars,  a 
satisfactory  repair  can  be  made  by  cutting  out  a  piece  of  the  loose  bar, 
inserting  a  turn-buckle,  and  drawing  it  up  to  the  same  tension  as  that  of  the 
tight  bar.  This  can  be  done  without  falsework,  but  traffic  must  be  kept 
off  the  bridge  while  work  is  in  progress.  The  same  procedure  can  also  be 
adopted  for  the  outside  bar  of  members  composed  of  more  than  two  bars, 
but  on  the  inside  bars  it  is  impracticable,  because  rivets  cannot  be 
driven. 

When  truss  bridges  are  more  heavily  loaded  than  was  originally  con- 
templated, the  overstress  is  likely  to  be  greatest  on  the  counters.  Also  on 
a  long  span  the  overstress  on  the  floor  system  is  liable  to  be  considerably 
greater  than  it  is  on  the  main  truss  members.  For  this  reason  it  is  often 
possible  to  make  the  structure  safe  for  considerably  heavier  loading  by 
reinforcing  these  parts  and  keeping  it  in  service  instead  of  replacing  with 
a  heavier  bridge.  Also  in  some  cases  it  is  possible  to  improve  the  struc- 
ture without  strengthening  it;  that  is,  on  a  very  light  bridge,  subject  to 
large  vibrations  under  trainloads,  it  is  practicable  to  improve  the  action  by 


424  ECONOMICS   OF  BRIDGEWORK  Chapter  XLI 

putting  in  suitable  bracing  that  will  decrease  the  vibrations  and  the  wear, 
although,  strictly  speaking,  it  will  not  strengthen  the  main  trusa 
members. 

This  dissertation  does  not  aim  to  describe  all  the  details  of  repairs  neces- 
sary for  bridges,  because  usually  special  problems  in  each  case  are  devel- 
oped; but  the  underlying  principle  of  economics  of  maintenance  of  bridges 
and  similar  structures  is  to  keep  a  close  watch  on  them  by  frequent  and 
thorough  inspection,  and  to  repair  promptly  any  damage  that  is  found. 
The  neglect  of  prompt  attention  on  a  structure  often  leads  to  much  unnec- 
essarily expensive  work  and  sometimes  to  the  development  of  dangerous 
conditions. 


The  joint  data  of  Mr.  Chalfant  and  Mr.  Covell  were  contained  in  two 
letters  from  which  the  following  extracts  have  been  made : 

The  subject  will  be  divided  for  convenience  into  three  parts,  viz: 

A.  Masonry. 

B.  Floors. 

C.  Painting. 

(A)     Masonry 

The  constant  tendency  of  small  streams  to  change  their  courses  necessi- 
tates regular  inspection  to  prevent  undue  scouring  and  cutting  of  the  banks 
and  approaches.  Where  the  nature  of  the  foundation  and  depth  of  masonry 
are  a  matter  of  record,  the  soundings  and  measurements  can  be  inter- 
preted with  comparative  ease,  but  where  this  knowledge  is  lacking,  as  is 
true  in  many  cases,  chances  should  not  be  taken.  Sometimes  barriers  of  a 
more  or  less  permanent  nature  can  be  erected  above  the  bridge  in  such  a 
manner  as  to  turn  the  stream  back  into  its  natural  channel,  or  the  channel 
itself  may  be  changed.  When  this  cannot  be  done,  heavy  rip-rap  should  be 
placed  around  the  masonry  in  such  a  manner  as  to  fill  the  hole  and  prevent 
further  erosion.  This  rip-rap  may  be  formed  of  rough  stones  from  the 
quarry  or  of  blocks  of  concrete  made  at  the  site.  When  concrete  is  used 
for  protection,  it  should  be  in  loose  blocks  which  are  free  to  settle,  rather 
than  in  a  solid  mass  which,  in  turn,  may  be  under-scoured. 

When  the  stream  is  of  sufficient  size  to  require  piers  in  the  channel,  with 
other  than  rock  foundations,  there  should  be  a  systematic  program  of  sound- 
ings so  that  the  conditions  of  the  stream-bed  around  the  piers  may  be 
known,  and  so  that  changes  may  be  noted.  This  is  essential  when  the 
masonry  rests  on  piles,  but  is  of  even  greater  importance  when  the  founda- 
tion consists  of  a  timber  grillage  on  gravel  or  other  hard  stratum.  Heavy 
rip-rap  is  a  most  excellent  protection  to  piers  against  scouring  of  the  bed  of 
the  stream;  but,  when  once  pla(;ed,  there  can  be  no  assurance  of  future 
security.  The  rip-rap  may  be  moved  by  ice  so  that  the  bed  around  the 
pier  is  again  ex])osed  to  erosion. 


ECONOMICS   OF  MAINTENANCE   AND   REPAIKS  425 

(B)    Floors 

When  the  strength  of  the  superstructure  will  admit  of  such  loading,  the 
roadway  floor  should  be  reconstructed  with  a  reinforced-concrete  slab  and 
brick  wearing  surface,  and  the  sidewalk  should  be  of  reinforced-concrete. 
In  some  cases,  where  new  steel  stringers  are  required,  buckle  plates  may  be 
used  with  some  form  of  comparatively-permanent  wearing-surface.  Where 
the  foot  traffic  is  heavy,  the  sidewalk  can  be  given  an  asphalt  wearing-sur- 
face. Few  of  the  older  bridges  are  heavy  enough  for  the  loading  indicated, 
having  been  originally  floored  with  plank.  The  time  for  use  of  a  timber 
floor  with  the  side  of  the  grain  exposed  to  wear  has  passed  in  most  places. 
The  spikes  work  up  and  cut  automobile  tires,  and  the  floor  soon  requires 
renewal.  Lumber  is  now  so  costly  that  it  is  not  usually  economical  to 
employ  untreated  timber  in  so  exposed  a  place  as  a  bridge  floor,  and  the 
use  of  treated  lumber  only,  with  wood-block  wearing-surface,  is  recom- 
mended. 

We  have  scores  of  iron  and  steel  bridges  over  rivers  and  small  streams, 
which  structures  are  too  light  to  carry  a  concrete  and  brick  roadway  floor 
or  a  concrete  sidewalk.  The  weight  of  trucks  now  traversing  these  bridges 
makes  the  use  of  wooden  stringers  very  undesirable  because  of  the  presence 
of  knots  and  other  defects,  hence  steel  stringers  are  employed.  The  prac- 
tice in  some  places  is  to  lay  planks  directly  on  the  steel  stringers  with  only 
occasional  fastenings,  but  this  does  not  seem  to  be  satisfactory.  Bolting 
at  each  bearing  point  is  expensive,  hence  our  practice  is  to  bolt  a  surfaced 
2f"X5"  naihng  piece  on  top  of  each  stringer,  nailing  the  planks  with 
two  nails  at  each  intersection,  as  in  the  case  of  wooden  stringers.  It  has 
been  found  that  such  solid  nailing  distributes  the  load  so  that  a  wheel  load 
is  carried  by  at  least  two  stringers.  On  such  bridges  the  stringers  should  be 
from  24"  to  28"  center  to  center;  and  planks  of  uniform  width,  at  least  10 
inches  wide  and  surfaced  to  2f  inches,  should  be  laid  parallel  with  the  back- 
walls,  even  though  the  skew  necessitates  extra-long  planks.  This  prevents 
pointed  ends,  which  are  hard  to  support.  In  extreme  cases  the  planks  may 
be  in  more  than  one  length  across  the  floor,  but  the  joints  in  adjacent  planks 
should  not  come  over  the  same  stringer  or  adjacent  stringers,  but  should 
lap  for  a  distance  equal  to  at  least  two  spaces  between  stringers. 

In  case  the  bridge  carries  street-car  traffic,  there  seems  to  be  no  better 
construction  than  to  employ  ties  to  support  the  rails  and  planks.  Seven- 
inch  grooved  rails  and  half-inch  tie  plates  are  used.  Planks  at  least  10 
inches  wide  and  surfaced  to  3f  inches  give  good  results.  The  blocks  should 
then  have  sufficient  depth  to  come  flush  with  the  rail.  A  shaped  wood-filler 
on  each  side  of  the  rail  is  much  lighter  and  more  permanent  than  concrete 
filling.  It  is  very  important,  however,  that  each  tie  shall  have  but  two 
bearings  and  that  the  rails  be  as  nearly  over  the  stringers  as  possible,  other- 
wise the  springing  and  warping  of  the  ties  wiU  give  an  irregular  bearing  for 
the  rails,  resulting  in  future  trouble.  In  this  connection  it  might  be  sug- 
gested that  all  street-car  rails  be  painfed,  when  laid,  like  all  other  struc- 


426  ECONOMICS  OF  BRIDGEWORK  Chapter  XLI 

tural  steel,  omitting  paint  from  the  head  if  desired.  The  rails,  in  many 
installations  where  the  traffic  is  comparatively  fight,  rust  out  in  the  web  and 
base,  rather  than  wear  out. 

Wood  blocks  may  be  laid  directly  on  the  planks,  but  the  usual  practice 
is  to  place  a  single  layer  of  tar  paper  between,  so  as  to  prevent  loss  of  the 
hot  joint-fiUer.  A  very  convenient  depth  for  the  wood  blocks  is  3|  inches, 
but,  whatever  depth  is  selected,  there  should  be  at  least  one-fourth  inch 
difference  between  the  depth  and  the  width,  so  that  they  wOl  not  be  laid 
accidentaUy  with  the  side  of  the  grain  up.  On  long  bridges,  especiaUy 
where  there  is  a  grade,  angles  should  be  fastened  to  the  floor  with  lag  screws 
at  intervals  varying  from  10  feet  to  30  feet,  according  to  conditions,  in  order 
to  prevent  the  blocks  from  creeping.  On  grades  greater  than  two  per 
cent,  "hniside"  blocks,  made  like  hillside  brick,  can  be  used  to  good  advan- 
tage. We  have  had  a  short  section  of  such  floor  in  place  on  an  eight  per 
cent  grade  for  several  years  with  good  success.  Where  there  are  no  street- 
car rails  to  prevent  side  drainage,  it  is  well  to  give  the  roadway  a  crown  of 
two  or  three  inches  in  order  to  assist  in  draining. 

While  it  is  true  that  the  floors  described  are  heavier  than  the  plank 
floors  which  they  replace,  this  is  offset  by  the  comparative  smoothness  of 
the  surface,  which  reduces  the  vibration  caused  by  passing  vehicles. 

The  sidewalks  on  our  lighter  bridges  have  been  constructed  with  either 
treated  or  untreated  lumber  laid  in  the  usual  manner,  but  this  is  not  very 
satisfactory.  Such  floors  wear  out  rapidly,  if  the  traffic  is  heavy,  and  are 
rough  and  irregular.  Treated  lumber  exposed  to  wear  on  the  side  of  the 
grain  does  not  last  well  and  does  not  make  a  good  sidewalk.  We  have 
recently  laid  a  sidewalk  on  a  river  bridge  with  tongued-and-grooved  lumber 
surfaced  to  If  inches,  and  with  wood  blocks  2  inches  deep,  3  inches  wide, 
and  averaging  6  inches  long,  laid  thereon.  Each  block  in  every  fifth  row 
was  nailed  with  a  lOd  wire  finishing  nail  to  prevent  movement  or  dis- 
placement, and  the  joints  were  filled  with  dry  sand.  It  was  found,  while 
the  work  was  in  progress,  that  blocks  of  this  depth,  on  a  surface  where 
there  was  no  wheel  traffic,  remained  loose  so  that  mischief -loving  boys  lifted 
them  out  of  the  walk  and  threw  them  into  the  river.  The  joints  were  then 
filled  with  hot  bituminous  filler,  as  was  done  on  the  roadway,  but  care  was 
taken  to  cover  the  surface  immediately  with  dry  sand  before  the  filler  had 
time  to  cool.     The  resulting  surface  is  very  satisfactory. 

When  the  old  plank  floors  on  the  smaller  bridges  are  replaced  with  the 
wood-block  floor  as  described,  the  grade  is  usually  raised  a  few  inches.  This 
necessitates  an  increased  height  in  the  back-wall.  At  first  this  was  accom- 
plished by  taking  up  the  sand-stone  back-walls  and  resetting  them  at  suffi- 
cient height  to  dress  to  the  new  floor-level.  This  is  expensive  and  not 
wholly  satisfactory;  and  for  three  years  the  same  result  has  been  reached 
by  cutting  the  old  ba(;k-wall  <lown,  where  necessary,  and  setting  two  rows 
of  paving  brick  at  right  angles  to  the  face  of  the  said  back-wall  in  a  bed  of 
Portland  cement  mortar,  and  grouted  in  place.     Where  the  approaches 


ECONOMICS   OF  MAINTENANCE   AND   REPAIRS  427 

have  an  earth  wearing  surface  they  are  raised  by  the  use  of  broken  stone; 
but  where  they  are  unproved  with  macadam,  bituminous  surfaces,  or  brick, 
a  brick  surface  is  used.  Bituminous  concrete  by  the  penetration  method 
and  Portland  cement  concrete  have  both  been  employed;  but  under  the 
conditions  prevailing  here,  neither  has  proved  satisfactory.  The  former 
requires  a  heavy  roller  to  give  good  results,  and  the  size  of  the  contract 
will  not  warrant  this;  and  the  latter  should  be  kept  free  from  travel  for 
a  longer  period  than  is  required  to  complete  all  the  rest  of  the  job.  Our 
practice  on  small  bridges,  in  all  cases  where  the  traffic  cannot  be  readily 
diverted,  is  to  cut  the  old  floor  in  half  and  put  in  the  new  stringers  and  nail- 
ing pieces  on  one  side.  A  temporary  floor  is  then  laid  on  this  side,  and  the 
stringers  and  nailing  pieces  are  put  in  on  the  other  side.  The  new  floor  can 
then  be  laid  without  serious  interruption  to  vehicle-traffic.  Foot-traffic  is 
maintained  continuously.  We  use  S^XS^^Xf-angle  wheel-guards  10 
inches  above  the  floor  in  all  through,  plate-girder  bridges  in  place  of  wooden 
wheel-guards. 

A  complete  itemized  record  of  the  repairs  on  each  floor  should  be  kept 
in  the  office.  A  brief  summary  of  this,  giving  the  date  and  extent  of  the 
repairs,  should  be  prepared  and  placed  in  the  hands  of  the  inspector  for  the 
annual  inspection  in  the  spring  or  early  summer.  This  is  especially  impor- 
tant in  the  case  of  ordinary  plank  floors.  When  the  inspection  is  made, 
any  accumulation  of  mud  or  dirt  should  be  cleaned  from  the  floor,  which 
should  then  be  carefully  examined  for  needed  repairs.  Ordinarily  it  is 
difficult  to  detect  decay  in  the  top  of  the  stringers,  until  the  hard,  sound 
shell  on  the  outside  breaks  down.  If  the  inspector  has  the  date  when  the 
stringers  were  put  in,  his  experience  will  tell  him  when  he  needs  to  expect 
this  kind  of  failure;    and  planks  should  then  be  taken  up  to  make  sure. 

Records  kept  in  this  manner  enable  the  person  in  charge  to  have  definite 
knowledge  of  the  conditions  in  the  field;  and  an  inspection  made  with  such 
information  at  hand  forestalls  many  floor  failures  which  otherwise  fre- 
quently occur. 

(C)     Painting 

We  have  found  that  our  painting  is  best  done  by  day  labor  with  paint 
furnished  by  the  owner.  It  frequently  happens  that  parts  of  the  bridge 
need  to  be  only  touched  up  at  various  points  for  the  first  coat,  in  order  to 
give  a  uniform  surface  over  the  whole  bridge;  and  the  extent  of  such  work 
cannot  well  be  specified  in  advance.  Cleaning  is  fully  as  important  as  the 
painting;  in  fact  paint  applied  over  rust,  scale,  or  dirt  is  worse  than  wasted, 
for  it  may  prevent  the  real  conditions  from  showing  and  thus  foster  further 
corrosion.  With  a  good,  conscientious  foreman,  the  cleaning  can  be  made 
more  thorough  than  is  usually  possible  under  any  inspector  with  contract 
work.  At  this  point  it  might  be  well  to  observe  that  many  detailers  seem  to 
forget  all  about  maintenance,  and  especially  about  cleaning  and  painting, 
when  the  drawings  are  made.     Clearances  are  too  small,  and  exposed  metal 


428  ECONOMICS   OF  BRIDGEWORK  Chapter  XLI 

is  placed  in  inaccessible  places.  This  can  sometimes  be  corrected  with 
concrete. 

A  painting  program  would  include  the  painting  of  small  bridges  in 
scattered  positions  every  three  or  four  years.  If  the  territory  is  extensive, 
it  should  be  divided  into  sections,  one  of  which  should  be  included  each 
year.  While  there  are  many  good  proprietary  paints,  there  is  no  very 
satisfactory  way  of  selecting  them  on  a  competitive  basis;  and  we  have 
found  it  better  to  purchase  the  paint  under  specifications  upon  which  all 
manufacturers  can  bid. 

Dark  paints  seem  to  be  more  durable  than  light  paints;  and  bridges 
which  are  lighted  at  night  can  be  painted  black  or  some  other  dark  color. 
Bridges  which  are  not  artifically  lighted  at  night  should  be  painted  a  light 
color  to  make  them  more  readily  visible.  Rather  than  paint  the  entire 
bridge  a  light  color,  the  floor  system  and  all  parts  below  the  usual  line  of 
vision  (parts  where  it  is  generally  most  difficult  to  maintain  paint)  may  be 
painted  dark.  When  a  new  floor  is  put  on,  the  tops  of  all  floor  beams,  side- 
walk brackets,  and  stringers,  and  other  parts  ordinarily  inaccessible  but 
made  accessible  during  this  work,  should  be  thoroughly  cleaned  and 
painted.  This  sometimes  involves  a  hardship  by  causing  delay  in  the  work 
when  traffic  is  maintained;  therefore,  instead  of  two  coats  of  paint,  a  heavy 
coat  of  red  lead  paste  can  be  used.  If  creosoted  lumber  is  to  come  in  con- 
tact with  steel,  the  ordinary  paint  will  not  stand,  as  creosote  is  a  solvent; 
hence  the  finishing  coat  should  be  a  specially-prepared,  acid-proof  paint. 

Where  the  finish  is  dark,  the  priming  coat  may  be  red  lead  and  linseed 
oil  paint;  and  where  the  finish  is  light,  a  good  priming-coat  pigment  is 
made  of  29%  lead  sulphate,  41%  lead  carbonate,  5%  zinc  chromate,  10% 
silica,  and  15%  asbestine.  A  good  black  finishing-coat  pigment  is  made  of 
55%  lamp-black  and  45%  special  French  ochre;  and  a  finishing-light-coat 
pigment  can  be  made  of  34%  lead  sulphate,  41%  lead  carbonate,  10% 
silica,  and  15%  asbestine,  with  sufficient  lamp-black  to  produce  a  pearl-graj^ 
color.  This  is  light  enough  to  be  readily  seen  and  stands  better  than 
pure  white.  The  vehicle  should  be  pure  linseed  oil  with  the  necessary 
drier.     All  proportioning  of  ingredients  should  be  by  weight. 

Where  possible,  all  steelwork  directly  over  steam-railroad  tracks  should 
be  protected  by  concrete  rather  than  by  paint.  Where  tliis  is  not  practica- 
ble, the  painting  should  be  done  at  more  frequent  intervals  than  is  ordi- 
narily necessary. 


The  preceding  records  of  the  opinions  of  four  engineers  who  are  experts 
on  maintenance'  and  repaii's  ought  to  afford  the  reader  sufficient  data  on  the 
sul)ject  to  serve  all  practical  ])ui])()se8.  There  is  some  unavoidable  repeti- 
tion involved,  and  there  ai-e  some  ininoi'  differences  of  ojiiniou,  because  the 
economics  of  niaiiiten;uice  and  r(^])airs  is  f;tr  fi'om  b(Mng  an  exact  science. 
Again,  the  tr(^atnunit  of  the  matter  of  jminting  encroaches  on  the  special 


ECONOMICS   OF  MAINTENANCE   AND   REPAIRS  429 

subject  of  the  next  chapter;  nevertheless,  it  was  not  considered  advisable  to 
omit  any  salient  portions  of  the  three  dissertations.  A  little  repetition  in  a 
technical  work  does  no  harm,  when  it  expresses  the  opinions  of  several 
authorities;  and  the  different  points  of  view  recorded  are  certainly  both 
interesting  and  advantageous. 


CHAPTER  XLII 


ECONOMICS    OF   METAL    PROTECTION' 


The  preservation  of  bridges  against  rapid  deterioration  is  just  as  impor- 
tant a  matter  as  ensuring  that  they  are  properly  proportioned  and  con- 
structed— yes,  even  more  important,  for  what  behooveth  it  the  owner  of  a 
steel  structure  to  take  the  utmost  care  in  its  designing  and  building,  if  he 
neglect  to  protect  it  effectively  against  the  ravages  of  rust?  The  life  of  a 
metal  bridge  that  is  scientifically  designed,  honestly  and  carefully  built, 
and  not  seriously  overloaded,  if  properly  maintained,  is  indefinitely  long, 
but  if  badly  neglected  is  often  quite  short,  especially  when  it  is  exposed  to 
acid  fumes,  such  as  those  contained  in  the  smoke  from  locomotives  passing 
through  or  beneath.  It  is  evident,  therefore,  that  the  subject  of  economics 
of  metal  protection  is  one  of  consequence  and  deserving  of  the  most  thor- 
ough consideration. 

It  may  appropriately  be  divided  into  two  topics,  viz.,  the  general 
question  of  economic  expediency  in  guarding  the  structure  against  injury 
by  the  expenditure  of  considerable  money,  and  the  cheapest  ways  of  effect- 
ing satisfactory  protection. 

The  first  topic  may  readily  be  disposed  of  by  the  statement  that  it  is  in 
the  line  of  true  economy  to  spend  whatever  amount  of  money  (within,  of 
course,  the  bounds  of  reason)  that  is  found  to  be  necessary  to  prevent  the 
starting  of  any  rusting  of  metal  whatsoever.  If,  as  many  people  think,  the 
life  of  a  steel  bridge  is  limited  to  two  or  three  decades,  the  economic  question 
would  arise  as  to  how  much  money  it  would  pay  to  spend  on  painting  or 
other  protection,  in  order  to  prolong  the  said  life  a  few  years;  but  such  is 
by  no  means  the  case,  because,  as  previously  indicated,  a  modern  steel 
bridge  ought  to  last  for  centuries. 

The  second  topic  covers  a  wide  field,  and  requires  to  be  treated  in  detail. 
The  principal  subjects  that  it  includes  are  the  following: 

1.  Best  kinds  of  paint  to  use  in  shop  and  field. 

2.  Best  vehicle  for  pigments. 

3.  Use  of  driers. 

'•'  After  this  ohapt(>r  had  Ix^en  finished  for  some  time  it  was  submitted  for 
criticism  to  the  veteran  paint  speciaUst,  Dr.  A.  11.  Sabin,  Consviltinp  Chemist  to  the 
National  Lead  Company,  and  the  a('knowl(>d.u;(Ml  dean  nf  Aineriean  i)aint  men.  Dr. 
Sabin  very  i\indly  prepared  some  memoranda  on  (■ertain  points;  and,  in  order  not  to 
necessitate  a  re-writing  of  the  entire  chapter,  his  .suggestions  have  been  incorporated 
as  foot-notes. 

430 


ECONOMICS   OF   METAL   PROTECTION  431 

4.  What  colors  for  paint  are  best  suited  to  different  conditions. 

5.  Elasticity  of  paint  coats. 

6.  Covering  and  spreading  powers  of  paints. 

7.  Cement  paints. 

8.  Linseed  oil  alone  for  the  shop  coat. 

9.  Climatic  influences  on  paints. 

10.  Application  of  paint  by  spraying. 

11.  How  best  to  prepare  new  metalwork  to  receive  the  shop  coat. 

12.  Pickling. 

13.  How  best  to  paint  newly-erected  metal. 

14.  Concrete  encasement. 

15.  Gunite. 

16.  Proper  treatment  of  steel  that  is  to  be  encased  in  concrete  or 

gunite. 

17.  'Water-proofing. 

18.  Protection  of  metal  against  brine  drippings. 

19.  Protection  of  metal  against  locomotive  gases. 

20.  Causes  of  paint  deterioration. 

21.  How  to  care  for  incipient  failure  of  paint. 

22.  How  to  determine  when  repainting  is  necessary. 

23.  How  to  clean  the  metalwork  preparatory  to  applying  a  new  coat 

of  paint. 

24.  Application  of  paint  after  field  cleaning. 

25.  Factors  that  affect  results  in  painting. 

26.  Economic  observations  concerning  painting  in  general. 

The  topics  in  the  above  list  will  be  taken  one  at  a  time  and  discussed 
from  the  economic  view-point. 

Best  Kinds  of  Paint  for  Shop  and  Field 

Concerning  the  best  kinds  of  paint  for  bridges  there  has  been  waged  a 
lively  war  of  competitors  during  half  a  century  or  longer,  each  one  claiming 
that  his  product  is  the  best.  Independent  engineers,  too,  have  varied  in 
their  views  thereon,  for  each  one  has  been  rather  prone  to  be  influenced  by 
his  own  personal  experience;  but  of  late  years  a  general  consensus  of 
opinions  has  been  reached,  the  decision  being  that  the  priming  or  shop 
coat  should  be  red-lead  paint,  the  first  field  coat  a  mixture  of  red-lead  and 
some  so-called  inert  material,  and  the  third  coat  a  carbon  or  graphite 
paint.  The  term  "inert"  as  applied  to  paint  constituents  was  originated 
some  thirty  years  ago  by  the  late  Dr.  Dudley.  It  reflects  his  idea  that 
lead  and  zinc  pigments  are  chemically  active  towards  linseed  oil,  while 
barytes,  silica,  etc.,  are  not.  As  a  matter  of  fact,  the  most  important,  if 
not  the  only,  relations  between  the  pigment  and  the  vehicle  are  physical, 
and  in  that  sense  there  are  no  inert  pigments.     Nothing  can  be  less  chem- 


432  ECONOMICS   OF   BRIDGEWORK  Chapter  XLII 

ically  active  than  powdered  quartz,  yet  it  will  bleach  oil  as  thoroughly  as  is 
possible  in  any  way. 

Some  valuable  suggestions  concerning  the  composition  of  shop  and 
field  coats  are  given  at  the  end  of  Chapter  XLI  in  the  data  supplied  by 
Messrs.  Chalfant  and  Covell. 

There  seems  to  exist  among  engineers  a  notion  that  it  is  unprofessional 
for  a  technical  writer  to  recommend  in  print  any  special  make  of  paint. 
Such  a  tenet,  however,  is  fundamentally  wrong,  as  is  also  the  idea  that  one 
should  not  call  for  any  particular  material  of  any  kind  in  his  specifications. 
If  an  engineer  is  confident  that  a  certain  material  will  suit  his  proposed 
construction  better  than  any  other,  he  should  have  the  courage  of  his  con- 
viction and  should  call  for  its  use,  even  if  he  has  to  run  the  risk  of  evil- 
minded  persons  insinuating  that  he  was  illegitimately  influenced  so  to  do. 
Similarly,  when  a  technical  writer  has  learned  from  long  experience  that 
certain  materials  are  best  for  certain  purposes,  he  should  be-  sufficiently 
brave  and  independent  to  give  to  his  brother  engineers  the  benefit  of  his 
accrued  knowledge. 

For  many  years  the  author  has  favored  red  lead  for  the  shop  coat, 
provided  that  it  were  honestly  manufactured,  honestly  mixed,  honestly 
applied,  and  honestly  dried  before  being  either  covered  or  subjected  to 
possible  abrasion.  Again,  experience  has  taught  him  that  the  pigment 
should  not  be  delivered  at  the  shops  as  a  powder  or  even  as  a  paste,  but  that 
the  paint  should  be  previously  mixed  and  ready  for  use;  because  the  cahber 
of  the  men  employed  for  shop-painting  is  generally  so  small  that  they  can- 
not be  trusted  properly  to  mix  the  paint,  hence  it  has  usually  occurred  that 
the  mixture  was  lumpy,  that  thinners  were  illegitimately  added,  and  that 
the  coating  was  daubed  on  the  steel  irregularly,  being  too  thick  in  some 
places  and  too  attenuated  in  others. 

Year  after  year  the  author  has  continued  his  search  for  an  ideal  shop 
coat;  and  it  was  not  until  a  short  time  ago  that  he  found  it  in  Dutch  Boy 
Red  Lead.  At  first  he  could  obtain  this  only  in  either  powder  or  paste 
form,  with  which  it  was  impracticable  to  obtain  perfect  results;  but  finally 
he  persuaded  the  manufacturers  to  furnish  it  ready  mixed,  using  to  one 
American  gallon  of  pure  raw  linseed  oil  twenty-eight  pounds  of  the  pigment 
thoroughly  incorporated  by  grinding  with  the  oil.  He  is  now  satisfied  that 
he  has  discovered  what  he  has  been  searching  for  during  more  than  three 
decades.  For  the  field  coat  he  has  had  the  most  satisfactory  results  with 
Gohccn's  Carbonizing  Coating,  Nobrac,  and  Detroit  Graphite,  although 
at  one  time  long  ago,  as  will  be  explained  further  on,  the  latter  paint 
failed  him. 

()th(M-  engineers  have  had  good  luck  with  other  finishing  coats — for 
instance,  those  recommended  by  Cheesnian  &  Elliot,  Lowe  Brothers' 
"Metalcote,"  and  Toch  Brothers'  "Tockohth."  Lowe  Brothers'  "Red 
Lead  Lute"  has  giv(m  good  satisfaction  as  a  slio]")  coat;  and  for  tlmt  ]inrpose 
many  users  pin  their  faith  on  Cheesman  &  Elliot's  No.  31  Red  Oxide.     A 


ECONOMICS   OF   METAL   PROTECTION  433 

quarter  of  a  century  ago  the  author  used  to  employ  the  last-mentioned 
paint  as  a  finishing  coat,  and  found  it  excellent;  but  for  a  shop  coat  he 
believes  that  nothing  is  as  good  as  truly-first-class,  red-lead  paints. 

Between  1906  and  1912  there  was  made,  on  the  Havre  de  Grace,  Md., 
bridge  of  the  Pennsylvania  Railroad  Company,  an  elaborate  and  exceed- 
ingly valuable  series  of  tests  of  nineteen  different  kinds  of  paint  under  the 
direction  of  certain  expert  engineers.  The  results,  as  reported,  emphasize 
the  fact  that  red-lead  paints  and  those  having  a  considerable  amount  of 
red  lead  in  their  composition  are  the  most  durable,  and  that  a  paint  in  which 
the  top  coat  is  strictly  a  preservative  cover  over  the  red-lead  coat  gives  the 
best  results  of  all,  and  justifies  the  well-known  philosophy  of  the  late  Mr. 
Houston  Lowe  regarding  protective  paints  for  steel. 

To  quote  the  exact  words  of  Mr.  Geo.  S.  Rice,  one  of  the  engineers  who 
reported  on  the  said  tests,  "this  philosophy  prescribes  the  production  of  a 
solid  and  sufficiently-elastic  foundation  with  rust-restraining  properties  by 
a  priming  coat  of  red  lead,  followed  by  a  transition  coat  intermediate 
between  the  primer  and  the  top  coat,  the  office  of  the  latter  being  essen- 
tially protective  of  the  undercoats." 

It  was  noticeable  in  the  test  that  the  paints  which  withstood  best  had 
in  all  instances  a  very  large  percentage  of  pigment  in  their  composition. 

The  winning  paint  in  the  competition  was  a  combination  of  the  kind 
just  described,  submitted  by  the  Lowe  Brothers  Company.* 

In  his  book  "Paint  for  Steel  Structures"  Mr.  Lowe  expresses  these 
conclusions: 

1.  That  the  priming,  or  first  coat  of  paint,  upon  any  surface  is  the 
most  important  one;  and  that  it  should  form  an  inhibitive,  firm,  unyield- 
ing, and  receptive  foundation  for  those  to  follow  it. 

2.  That  under-coats  should  dry  harder  and  more  quickly  than  those 
above  them,  and  that  the  difference  in  drying  between  adjoining  coats 
should  not  be  very  great. 

3.  That  the  quality  of  the  binder  is  equally  as  important  as  the 
quality  of  the  pigment. 

4.  That  the  quantity  or  weight  of  pigment  used  is  equally  as  impor- 
tant as  its  quaUty  or  volume. 

5.  That  the  time  and  method  of  application  are  equally  as  impor- 
tant as  the  quality  of  the  paint. 

There  used  to  be  some  well-founded  objections  to  red-lead  paints  in 
general,  and  these  still  hold  good  against  the  cheap  varieties  thereof. 
The  principal  ones  were  a  tendency  to  sag  and  run  on  vertical  surfaces,  and 


*  This  statement  is  on  the  authority  of  Lowe  Brothers'  written  claim,  but  it  has  been 
contradicted  by  Dr.  Sabin,  who  says  that  the  winning  paint  was  a  pure  red  lead  man- 
ufactured by  the  National  Lead  Company.  Dr.  Sabin  prefers  to  use  red-lead  paint 
for  all  three  coats  instead  of  for  the  shop  coat  only,  in  spite  of  the  very  prevalent  idea 
that  red  lead,  for  efficiency,  should  be  covered  by  a  more  elastic  pigment. 


434  ECONOMICS   OF  BRIDGEWORK  Chapter  XLII 

to  settle  into  a  hard  mass  in  the  bottom  of  the  container.  These  faults  were 
due  to  an  excessive  amount  of  Utharge  in  the  pigment,  sometimes  as  much 
as  thirty  per  cent.  Within  a  few  years  certain  lead-paint  manufacturers 
have  reduced  the  Utharge  to  as  low  as  two  per  cent,  the  remaining  ninety- 
eight  per  cent  being  true  red  lead,  Pb304.  This  makes  an  ideal  paint  for 
the  priming  coat;  for,  being  extremely  fine,  it  fills  aU  pores,  and  brushes  out 
in  a  smooth,  even  film  free  from  voids.  Moreover,  it  stays  in  place  on 
vertical  surfaces,  does  not  act  ropy  under  the  brush,  and  does  not  settle  to 
the  bottom  of  the  container.  It  is  sold  generally  in  paste  form;  but,  until 
it  can  be  regularly  furnished  ready-mixed  for  apphcation,  it  v-ill  not  have 
attained  its  acme  of  excellence. 

The  amount  of  red  lead  to  be  used  per  American  gallon  of  vehicle  is 
stni  a  disputed  point  among  engineers.  In  some  cases  the  amoimt  actually 
employed  has  been  as  high  as  thirty-seven  pounds;  but  such  an  unusually 
great  quantity  cannot  be  made  to  give  satisfactory  results,  unless  all  the 
conditions  are  ideal.  If  the  paint  be  appHed  under  contract,  which  is  by 
no  means  the  best  way  but  sometimes  is  unavoidable,  it  is  well  to  limit  the 
amount  of  pigment  to  twenty-eight,  or  possibly  thirty,  pounds  per  gallon 
of  oil. 

The  theory  one  should  adopt  when  applying  the  coats  which  follow  the 
priming  coat,  as  well  as  at  any  time  thereafter  when  the  bridge  is  to  be 
repainted,  is  to  have  each  coat  more  elastic  than  the  one  preceding  it,  so 
as  to  insure  against  checking  and  alligatoring — a  term  very  aptly  apphed 
to  what  occurs  when  paint  dries  in  lumps  or  ridges  or  when  it  shows  wide, 
irregular  cracks,  giving  the  surface  an  appearance  of  alligator  hide. 

Some  authorities  advise  adding  a  little  non-drying  oil  to  the  final  coat 
of  paint,  in  order  to  enable  it  better  to  shed  water;  and  the  author  agrees 
with  this  practice,  provided  that  the  amount  used  be  not  great  enough  to 
prevent  the  paint  from  drying  thoroughly  by  the  time  an  additional  coat  is 
required. 

Summing  up  the  matter  of  the  best  kinds  of  paint  for  bridgework,  the 
author  feels  that  he  cannot  do  better  than  to  quote  the  following  from  Mr. 
Houston  Lowe's  ''Paints  for  Steel  Structures"  concerning  the  desirable 
features  of  an  anti-corrosive  metal  coating: 

1.  It  should  hide  the  surface. 

2.  Should  cement  itself  together,  and  also  cement  itself  to  either 

damp  or  dry  metallic  surfaces. 

3.  Should  expand  and  contract  without  breaking  its  own  body. 

4.  Should  present  a  hard,  yet  tough,  outer  surface. 

5.  Should  be  impervious  to  water,  carbonic  acid,  or  other  gases. 

6.  Should  be  unaffected  by  sunshine,  heat,  frost,  dew,  or  climatic 

changes. 

7.  Should  be  unaffected  by  ordinary  mechanical  abrasion. 

8.  Should  wear  evenly. 


ECONOMICS   OF  METAL   PROTECTION  435 

9.  Should  fail  by  gradual  wear,  not  by  disintegration. 

10.  Should  leave  a  good  surface  for  repainting, 

11.  Should  not  require  an  unreasonable  amount  of  skill  or  muscle  in 
I  application. 

12.  Should  be  homogeneous. 

13.  Should  dry  fast  enough. 

14.  Should  not  be  readily  ignited. 

15.  Should  have  power  to  absorb  and  remove  moisture  or  dampness 

from  the  metal. 

16.  Should  have    properties  that  will  prevent    corrosive  action  of 

traces  of  water  in  contact  with  the  metal. 

Best  Vehicle  for  Paint 

Durability  of  paint  depends  just  as  much  upon  the  vehicle  as  it  does 
upon  the  pigment.  Up  to  the  present  time  no  vehicle  has  proved  to  be 
anything  hke  as  good  as  pure,  raw,  linseed  oil,  notwithstanding  the  fact 
that  many  substitutes  have  been  tried.  Some  of  these  substitutes  are 
valuable  as  thinners  of  linseed  oil,  if  used  in  moderate  quantity,  because 
they  often  improve  somewhat  both  its  drying  and  its  working  properties. 
The  usual  reason,  however,  for  the  adoption  of  such  thinners  or  adulterants 
is  to  reduce  the  cost  of  the  paint;  and  too  often  this  is  done  at  the  expense 
of  its  quality.  It  is  generally  conceded  that  ''the  base  of  the  best  substi- 
tutes for  linseed  oil  is  linseed  oil  itself." 

The  author  once  had  great  hope  of  Leucol  Oil  as  a  vehicle;  and,  as  a  test 
of  it,  he  used  Leucol  Red-Lead  Paint  on  one  of  his  Mexican  bridges  in  com- 
petition with  a  number  of  other  paints  on  several  nearby  structures;  but 
it  failed  to  give  satisfactory  results,  the  surface  quickly  assuming  a  whitish 
tinge,  and  the  protection  failing  much  sooner  than  it  should  have.  It 
should  be  stated,  though,  that  the  climatic  conditions  in  the  tierra  caliente 
where  these  structures  were  located  were  unusually  severe  for  bridge 
paints.  All  but  one  of  the  paints  then  tested  failed  unequivocally — but 
of  that  exception,  more  anon. 

Boiled  linsesd  oil  was  much  used  for  bridge  paint  in  times  long  past; 
but  experience  has  shown  that  the  boiUng  is  a  detriment  to  the  vehicle 
instead  of  an  improvement  thereto. 

Use  of  Driers  ■ 

Some  engineers  consider  all  driers  merely  as  adulterants,  employed  solely 
for  the  purpose  of  cheapening  the  product;  but  the  author  is  of  the  opinion 
that  they  occupy  a  legitimate  place  in  paint  manufacture,  provided  they 
be  used  in  moderation — especially  for  priming  and  intermediate  coats, 
which  often  need  to  dry  fairly  quickly  in  order  not  to  delay  the  application 
of  the  succeeding  coat.    As  far  as  he  knows,  the  best  drier  to  employ  is 


436  ECONOMICS   OF   BRIDGEWORK  Chapter  XLII 

Sipe's  Japan  oil,  most  of  the  other  driers  being  a  detriment  rather  than  a 
help,  especially  to  red-lead  paints.* 

Best  Colors  for  Paints 

Practice  seems  to  have  decreed  that  dark  paints  are  more  suitable  for 
bridges  than  light  ones,  notwithstanding  the  well-known  facts  that  they 
absorb  much  heat,  and  that  excessive  heat  is  one  of  the  most  active  agencies 
in  paint  deterioration.  The  main  reason  for  the  reluctance  to  use  light 
paints  is  their  tendency  to  fade  and  to  show  the  dirt  that  inevitably  accu- 
mulates on  all  bridge  metal;  but  the  fading  is  avoidable  by  a  proper  study 
of  the  finishing  coat,  and  it  cannot  be  denied  that  dirt  shows  more  or  less 
on  dark  paints  as  well  as  on  light  ones.  It  must  not  be  forgotten  that  the 
selection  of  paint  color  for  any  bridge  is  a  matter  of  aesthetics  as  well  as  of 
expediency;  for  in  some  structures  dark  colors  give  the  finer  effect,  and  in 
others  light  ones  provide  a  better  appearance.  An  old  favorite  color  of  the 
author's  is  olive  green;  and  he  has  employed  it  on  a  number  of  occasions 
with  satisfaction  to  all  concerned.  Canary  yellow  and  pearl  gray  are  often 
suitable  colors  for  the  finishing  coat. 

There  is  one  important  point  about  paint  colors  that  should  never 
be  ignored,  viz.,  that,  no  matter  how  many  coats  are  given  to  any  steel- 
work, all  of  them  should  be  of  essentially  different  shades  or  colors,  in  order 
to  make  sure  that  all  the  coats  called  for  are  really  applied.  In  one  of  his 
early  bridges,  the  author  caught  the  erection  superintendent  trying  to 
palm  off  on  him  a  single  coat  of  rather  thick  paint  instead  of  two  field  coats 
of  the  same  color.  Ever  since  then  his  bridge-erection  specifications  have 
called  for  distinctly  different  shades  or  colors  of  paint  coats. 

Elasticity  of  Paint  Coats 

The  matter  of  elasticity  in  paint  coats  is  one  of  extreme  importance; 
because,  if  neglected,  the  paint  is  liable  to  crack  and  permit  moisture  to 
reach  the  metal,  thus  starting  rust.  As  before  indicated,  there  should  be  a 
gradual  increase  in  the  elasticity  of  the  different  coats  from  the  priming  one 
outward. 

Covering  and  Spreading  Powers  of  Paints 

One  of  the  most  effective  claims  of  paint-selling  agents  is  that  the 
special  paint  which  they  handle  has  a  very  lai-ge  spreading  power;  and  this 

*Concerning  driers  Dr.  Sabin  writes  as  follows: 

Three  or  four  years  ago  I  sent  a  circular  letter,  asking  confidential  opinions  as  to 
driers,  to  about  a  dozen  of  the  chemists  of  the  really  big  mixed-paint  companies.  >\'ith- 
out  exception  they  agreed  that  if  price  is  left  out  of  account  the  best  drier  is  free  from 
rosin,  and  contains  lead  and  manganese,  from  three  lo  tw only-five  times  as  nnich  lead 
as  manganese,  but  must  contain  both. 

1  myself  would  not  object  to  a  drier  made  by  a  r(>s)ionsible  concern,  whic^h  con- 
tained a  little  rosin,  as  most  commercial  driers  do.     The  trouble  is  to  draw  the  line. 


ECONOMICS   OF   METAL   PROTECTION  437 

appeals  strongly  to  most  of  their  buyers — usually  erection  contractors — who 
recognize  that  the  greater  the  spreading  power  the  smaller  the  quantity 
of  paint  required,  and,  consequently,  the  less  the  cost.  The  bridge  owner, 
on  the  contrary,  is  not  interested  in  having  his  contractor  use  paint  of  the 
greatest  possible  spreading  capacity,  because  the  greater  the  said  capacity 
the  thinner  the  coating — and  the  thinner  the  coating  the  sooner  will  it 
become  disintegrated  by  moisture,  gases,  etc.  Of  course,  one  can  go  to 
the  other  extreme  by  laying  on  the  coat  too  thick,  in  which  case  it  will  run 
on  vertical  surfaces  and  will  be  too  slow  in  drying  on  horizontal  ones. 
Ordinarily,  single  coats  of  dried  paint  vary  in  thickness  between  one  five- 
hundredth  and  one  one-thousandth  of  an  inch;  and  to  produce  this  the 
spreading  capacity  is  from  eight-hundred  to  sixteen-hundred  square  feet 
per  American  gallon  of  paint.*  The  inspector  of  painting  on  bridgework, 
acting  solely  in  the  interests  of  the  owner,  should  endeavor  to  have  all  paint 
apphed  just  as  thickly  as  it  can  be  used  without  flowing  on  vertical  surfaces. 
It  should  be  daubed  on  thick  at  first,  then  gradually  worked  out  by  careful 
brushing  so  that  it  will  flow  into  all  the  pores  of  the  metal. 

Distinction  should  be  drawn  between  covering  capacity  and  spreading 
capacity  of  paints.  The  former  refers  to  the  hiding  capacity  of  the  coating 
in  relation  to  the  surface  on  which  it  is  apphed,  and  is  measured  by  certain 
standard  tests  on  white  surfaces,  while  the  spreading  capacity  refers  to  the 
number  of  square  feet  of  surface  that  can  be  covered  by  an  American  gallon 
of  the  paint. 

Cement  Paints 

Portland  cement  as  a  pigment  in  bridge  paints  has  begun  to  come  into 
vogue  of  late  years,  the  principal  manufacturers  of  it  being  the  well-known 
firm  of  Toch  Brothers,  and  their  product  being  designated  "Tockolith." 
The  author  has  not  yet  tried  this  brand  of  paint  on  any  of  his  bridges,  hence 
cannot  speak  from  personal  experience  concerning  its  efficacy;  but  the  fact 
that  such  a  prominent  bridge  engineer  as  Dr.  Gustav  Lindenthal  has  used 
it  on  some  of  his  largest  structures  is  a  guarantee  that  it  is  a  first-class 
protective  agent.  However,  Dr.  Lindenthal  is  not  willing  to  go  so  far  as 
to  state  that  Tockolith  is  superior  to  red-lead  paints  of  best  quaHty;  for 
the  author  asked  him  the  direct  question  and  he  would  not  reply  affirma- 
tively. Toch  Brothers  have  issued  a  very  interesting  little  pamphlet 
"R.I.W.  Steel  Preservative  Paints"  (R.I.W.  meaning  "Remember  It's 
Waterproof) ;  and  the  reader  is  referred  to  that  publication  for  further  infor- 

*  Dr.  Sabin  prefers  to  adopt  an  area  of  700  square  feet  per  gallon  of  paint  for  red 
lead  coatings,  and  states  that  graphite  paints  are  supposed  to  cover  from  350  to  600 
square  feet  per  gallon.  He  claims  that  red  lead  makes  a  stronger  and  more  impervious 
film  than  anything  else,  hence  can  be  safely  put  on  thinner,  and  that  three  red  lead 
coats,  covering  700  square  feet  per  gallon,  make  a  final  film  seven  one-thousandths  of  an 
inch  thick. 


438  ECONOMICS   OF   BRIDGEWORK  Chapter  XLII 

mation  on  the  subject.  If  the  claims  made  by  its  writer  are  correct, 
Tockohth  has  all  other  paints  beaten  for  bridgework. 

Speaking  of  the  claims  of  paint  manufacturers  and  agents  concerning  the 
excellence  of  their  products,  reminds  the  author  of  an  amusing  storj^  once 
told  him  by  Dr.  Sabin;  and,  as  it  has  never  yet  appeared  in  print,  it  is 
here  put  on  record. 

The  late  Mr.  D.  D.  Carrothers,  of  the  Baltimore  and  Ohio  Railway, 
used  to  tell  of  a  well-known  paint  manufacturer,  a  most  accomplished  and 
adroit  salesman,  who  persuaded  him  to  buy  a  considerable  quantity  of 
bridge-paint,  which  did  not  turn  out  well.  When  he  came  around  the  next 
year,  the  engineer  told  him  to  get  out;  his  paint  was  worthless.  "I  tnow 
that,"  was  the  unexpected  reply;  ''don't  you  suppose  I  know  all  about 
my  own  paint?  We  tested  that  paint  thoroughly,  as  I' thought;  but,  when 
it  came  to  practical  use,  it  developed  unforeseen  defects,  and  I  have  had 
trouble — the  utmost  trouble — in  finding  their  cause.  But  we  have  found 
and  corrected  it,  and  now  I  have  a  paint  that  is  absolutely  all  right;  but  I 
had  a  dreadful  time  with  it  last  year."  He  was  so  plausible,  convincing, 
and  persistent  that  he  went  away  with  another  good  order;  which,  however, 
turned  out  no  better  than  the  first  lot.  "But,"  said  Mr.  Carrothers,  "I 
expect  he  will  sell  me  some  more  this  year! " 

Linseed  Oil  alone  for  Shop  Coat 

A  quarter  of  a  century  ago  it  was  quite  usiial  to  employ  boiled  linseed  oil 
without  any  pigment  therein  for  the  shop  coat  on  structural  steelwork; 
and,  in  conformity  with  the  fashion,  the  author  followed  the  custom  when 
building  the  Union  Loop  and  the  Northwestern  Elevated  Railroads  of 
Chicago.  In  so  doing  he  learned  by  sad  experience  the  fallacy  of  the 
practice;  for,  owing  to  a  sudden  shortage  of  funds,  the  Company  had  to 
close  down  all  work  instanter,  leaving  a  mile  or  more  of  metalwork  erected 
and  unpainted.  When  construction  was  resumed  a  year  or  two  later  the 
steel  was  in  an  awful  mess,  and  required  an  immense  amount  of  labor  to 
clean  it.  In  all  probability,  that  portion  of  the  structure  actually  lost  a 
portion  of  its  vitality  through  this  unfortunate  circumstance.  Thereafter, 
of  course,  the  author  refused  to  allow  linseed  oil  alone  to  be  used  for  a  shop 
coat;  and  eventually  the  custom  went  out  of  fashion. 

Climatic  Influences  on  Paints 

Two  decades  ago  very  few  persons  recognized  that  climate  had  anything 
to  do  with  the  durability  of  ])ridge  paint,  and  that  a  brand  which  was 
effective  in  one  locality  might  fail  uttei-ly  in  another,  even  if  the  material 
were  taken  from  the  same  Ijarrcl.  During  the  Into  nineties  the  author 
secured  very  good  results  from  the  Detroit  Superior  Ca-aphite  paint,  finding 
that  it  could  be  relied  upon  for  five  years  before  a  new  coat  was  needed. 
All  the  bridges  where  he  em))loyed  it,  however,  were  located  in  the  north 


ECONOMICS   OF   METAL   PROTECTION  439 

until  he  built  one  across  the  Red  River  at  Alexandria,  La.  About  the  same 
time  he  was  constructing  over  two  hundred  bridges  on  the  line  of  a  certain 
Mexican  railway;  and,  although  he  experimented  there  with  a  number  of 
paints,  he  used  at  first  the  Detroit  product  on  most  of  the  metalwork,  for 
i?he  reason  that  it  had  given  him  such  satisfaction  previously.  It  had  not 
been  applied  in  the  field  on  these  Mexican  bridges  more  than  a  year  before  it 
began  to  fail  and  to  go  to  pieces  rapidly ;  and  about  the  same  time  the  paint 
on  the  Alexandria  bridge  showed  rapid  deterioration. 

Of  course,  other  paints  were  immediately  adopted  for  the  remaining 
Mexican  bridges;  and  the  manufacturers  of  the  Detroit  paint  were  noti- 
fied of  the  trouble.  In  consultation  it  was  decided  that  the  paint  fur- 
nished by  the  company,  while  excellent  for  dry  climates,  was  unsuited  for 
very  damp  ones,  especially  where  the  dampness  was  combined  with  heat. 
Thereupon  the  Company  instituted  an  elaborate  and  extensive  series  of 
practical  tests,  and  learned  therefrom  how  to  manufacture  paints  suited 
to  all  kinds  of  climates,  thus  regaining  for  their  product  the  high  reputation 
for  excellence  which  it  had  previously  enjoyed.  Today  it  is  one  of  the  best 
finishing  coats  for  bridges  that  the  market  affords;  but  the  Company's 
agents  are  now  very  careful  to  enquire  where  any  paint  is  going  to  be  used 
before  they  sell  it. 

Of  all  the  paints  tested  on  the  Mexican  bridges  previously  referred  to, 
there  was  only  one  that  proved  satisfactory  for  the  damp  climate  of  the 
tierra  caliente;  and,  strange  to  say,  that  one  was  located  in  the  worst  pos- 
sible place  for  paint  endurance,  viz.,  close  to  the  elevation  of  the  salt  water 
of  the  Gulf  of  Mexico  at  the  very  mouth  of  a  river  and  not  far  from  the  city 
of  Vera  Cruz— a  place  noted  for  its  disagreeable,  muggy  climate.  The 
paint  referred  to  was  Z.  P.  Leiter's  "Air-Drying,  Salt- Water-Proof  Paint." 
It  had  proved  to  be  the  best  of  some  twenty  standard  paints  tested  at 
Tampico,  Mex.,  for  a  large  wharf  there  by  the  late  A.  J.  Tullock,  a  noted 
bridge  contractor  and  the  founder  of  the  present  Missouri  Valley  Bridge 
Company  of  Leavenworth,  Kan.  It  was  because  of  Mr.  TuUock's  recom- 
mendation that  the  author  tried  it  at  Boca  del  Rio. 

Some  six  years  or  more  after  the  bridge  was  built  and  finally  painted,  the 
author  received  a  letter  from  the  General  Manager  of  the  railroad  company 
asking  the  name  of  the  brand  of  the  paint,  and  stating  that,  in  spite  of  its 
being  often  drenched  with  salt  spray,  it  appeared  to  be  in  as  good  condi- 
tion as  new  paint.* 

Soon  after  that  the  author  was  engaged  on  the  building  of  an  important 
bridge,  having  the  bottom  chords  quite  close  to  the  salt  water,  at  Vancou- 
ver, B.  C. ;  and,  naturally,  he  arranged  to  use  the  Leiter  paint.  The  metal- 
work  was  being  manufactured  in  the  shops  of  the  Dominion  Bridge  Com- 

*  It  has  been  stated  that,  since  the  death  of  Mr.  Leiter,  the  formula  for  his  Air- 
Drying,  Salt- Water-Proof  Paint  has  been  lost.  If  such  be  the  case,  it  is  truly  regret- 
table, for  it  certainly  was  a  most  effective  protection  to  steel  against  the  attacks  of  salt- 
water. 


440  ECONOMICS   OF  BRIDGEWORK  Chapter  XLII 

pany  near  Montreal,  during  the  winter;  and,  when  the  paint  was  applied 
to  the  cold  steel,  it  would  not  adhere,  consequently  another  brand  had  to 
be  employed. 

Mr.  Howard  P.  Quick,  Consulting  Engineer,  formerly  Mechanical 
Engineer  and  Designer  for  the  Pearson  Engineering  Corporation  and  Asso- 
ciated Companies  in  Brazil,  Mexico,  Canada,  Spain,  and  the  United  States, 
has  very  kindly  furnished  the  author  with  the  following  information  con- 
cerning the  developing  of  a  suitable  paint  for  steelwork  of  all  kinds  to  meet 
the  abnormal  climatic  conditions  of  Brazil  at  a  place  where  no  paint  of  any 
kind  imported  from  either  America  or  Europe  could  endure  the  tropical 
humidity.  Various  American  engineers  on  Brazilian  Constructions,  recog- 
nizing the  gravity  of  the  situation,  combined  forces,  and  had  the  chemists 
of  the  Rio  Janeiro  Gas  Company  experiment  for  them  in  their  search  for 
a  paint  that  would  meet  the  conditions.  That  company  possessed  an  up- 
to-date,  by-products,  coke-retort  system,  and  produced  therefrom  plenty 
of  tar  and  other  residues;  consequently  its  chemists  set  to  work  investi- 
gating the  question  on  the  basis  of  utilizing  these  by-products,  and  finally 
developed  a  tough,  adhesive,  elastic,  and  glossy-surfaced  paint  which  had 
all  the  qualities  desired,  barring  appearance.  The  composition  as  reported 
to  Mr.  Quick  by  the  American  Chemist,  Dr.  Harrop,  General  Manager  of 
the  Sodete  Anonyme  du  Gaz,  was  as  follows: 

1  part  of  Portland  cement. 
1  part  of  kerosene,  and 
4  parts  of  gas-works  tar. 

The  cement  was  first  mixed  with  the  kerosene,  and  then  tar  was  added 
to  develop  the  consistency  required.  This  produced  a  glossy,  quick-drying 
paint  of  a  dark,  greenish-black  color  which  dried  as  hard  as  rock  and  was 
unaffected  by  weather  or  temperature  changes. 

Such  a  paint  ought  to  be  quite  inexpensive;  and  it  should  be  tried  in 
other  tropical  climates  than  that  of  Brazil  and  also  in  the  Gulf  States  of  the 
U.  S.  A.  The  author  surmises  that  it  might  not  withstand  well  the  cold 
winters  of  our  northern  states;  but  it  would  be  well  to  give  it  a  trial  there. 

To-day  all  first-class  paint-manufacturers  recognize  that  it  is  absolutely 
essential  to  know  about  the  peculiarities  of  the  climate  where  any  structure 
is  to  be  erected  before  starting  to  manufacture  the  field  coats  of  paint 
therefor. 

Spraying  of  Paint 

Spraying  paint  on  bridge  metal  is  a  lately-developed  custom;  and  con- 
cerning the  satisfactoriness  of  the  process  there  are  both  pros  and  cons.  It 
involv(!S  a  wastage  of  paint  that  is  unavoidable^  but  which  may  be  kept 
down  to  r(!asona])le  limits  by  constant  care  and  attention;  and  it  is  claimed 
by  some  painters  that  it  does  not  work  the  paint  into  the  pores  of  the  metal 


ECONOMICS   OF   METAL   PROTECTION  441 

as  well  as  does  first-class  brushwork.  Again,  spraying  is  a  messy  process, 
and  much  paint  is  likely  to  go  to  places  for  which  it  was  not  intended.  One 
great  advantage  which  it  has  is  that  it  will  reach  locations  difficult  of  access 
by  the  brush,  and  which,  in  consequence,  are  often  improperly  protected. 
As  far  as  ultimate  total  cost  is  concerned,  it  is  probable  that  the  saving  in 
labor  will  about  offset  the  wastage  of  paint. 

Cleaning  of  Metalwork  for  Shop  Coat 

Unless  metalwork  is  thoroughly  cleaned  before  the  shop  coat  of  paint  is 
appHed,  the  endurance  of  the  protection  will  be  short;  hence  it  is  truly 
economic  to  ensure  that  the  cleaning  is  effectively  done,  so  as  to  remove  all 
dirt,  rust,  scale,  and  grease.  The  time  elapsing  between  cleaning  and 
painting  should  be  made  as  short  as  possible;  because  it  does  not  take  long 
to  start  fresh  rusting  on  cleaned  metal.  As  to  the  methods  for  shop-clean- 
ing, hand-work  ought  to  suffice;  for  sand-blasting  should  be  unnecessary. 
If  the  metal  is  very  badly  rusted,  it  generally  establishes  sound  evidence  of 
carelessness  on  the  part  of  somebody  who  ought  to  be  held  responsible  for 
its  injured  condition. 

Strictly  speaking,  all  rolled  material  for  bridgework  should  be  taken 
from  the  mill  to  the  shops  with  the  least  possible  delay,  and  should  be  stored 
under  proper  shelter  from  the  elements,  in  order  to  avoid  rusting;  and  it 
would  be  in  the  line  of  true  ultimate  economy  to  give  it  a  coat  of  linseed  oil 
soon  after  it  comes  from  the  rolls.  Most  steel  manufacturers  and  users 
will  claim  that  these  precautions  are  unnecessary,  that  the  coat  of  oil  would 
be  troublesome  to  put  on,  and  that  the  storage  sheds  would  cost  a  lot  of 
money.  These  objections,  of  course,  are  important;  but  the  author  is  of 
the  opinion  that,  in  the  interest  of  true  economy,  they  will  ultimately  be 
overcome,  and  that  sometime  in  the  future  all  proper  precautions  will  be 
taken  on  important  steel  structures  to  protect  effectively  against  rust  the 
metal  that  is  to  be  employed  in  their  manufacture. 

The  torch  should  first  be  used  freely  in  cleaning  metal  in  the  shops,  for 
the  double  purpose  of  burning  any  grease  that  there  may  be  on  it  and  to 
remove  all  moisture;  after  which  should  follow  scraping  with  steel  brushes, 
file  scrapers,  and  putty  knives.  Any  heavy  seed  rust  which  has  formed 
cups  in  the  metal  should  be  chipped  out  by  hammer,  care  being  taken  to 
avoid  all  unnecessary  cutting  of  the  steel.  This  cleaning  should  be  most 
carefully  watched  by  a  competent  and  reliable  inspector  whose  compen- 
sation comes  wholly  from  the  owner;  but  too  often  it  is  done  in  a  careless 
or  perfunctory  manner  by  ignorant  foreigners  who  take  no  interest  in  per- 
forming their  work  well.  It  used  to  be  the  custom  in  some  bridge  shops 
to  turn  over  the  painting  to  newly-imported  Hungarians,  who  were  the 
cheapest  laborers  on  the  pay-roll;  and,  as  a  result,  the  author  has  seen 
metal  delivered  at  site  with  the  shop  coat  of  paint  overlying  in  large  areas 
half  an  inch  of  frozen  mud.     Conditions  in  this  respect  today  are  undoubt- 


442  ECONOMICS   OF   BEIDGEWORK  Ch.\pter  XLII 

edly  much  better  than  they  were  twenty-five  or  thu-ty  j^ears  ago,  but  there 
is  still  much  room  for  improvement. 

Pickling 

Pickling  is  an  effective  way  to  clean  steel;  and  it  is  much  used  in  electro- 
plating and  enameling,  but  not  for  bridgework.  The  reason  is  the  trouble 
and  expense  which  it  involves.  In  applying  the  method,  it  must  be 
remembered  that  when  metal  is  immersed  in  a  hot  bath  of  either  sulphuric 
acid  or  muriatic  acid,  it  will  be  necessary,  immediately  after  removal  there- 
from, to  neutralize  any  portion  of  the  Kquid  which  adheres  to  the  steel. 

Painting  Newly-erected  Steelwork 

As  soon  as  practicable  after  a  span  is  erected,  provided  the  weather  is 
propitious  for  painting,  the  metal  should  be  thoroughly  cleansed  from  any 
dirt,  grease,  rust,  or  other  impurity  which  it  has  taken  on  since  leaving  the 
shop;  and  if,  for  any  reason,  any  serious  rusting  has  started,  all  traces  of  it 
should  be  removed.  Next,  all  spots  abraded  either  by  accident  or  during 
cleaning  should  be  touched  up  with  some  of  the  red-lead  paint  used  in  the 
shop  (with,  perhaps,  the  addition  of  a  little  Japan  drier  in  order  to  hasten  the 
job) ;  and,  after  this  spotting  has  dried  sufficiently,  the  first  field  coat  should 
be  applied.  This  should  be  allowed  ample  time  to  dry  before  the  next  coat 
is  put  on. 

Concrete  Encasement 

The  encasing  of  bridge  metal  in  concrete  is  an  expedient  which  has 
come  into  vogue  of  late  years.  It  is  employed  in  most  cases  for  protecting 
all  metal  below  the  level  of  the  deck  against  locomotive  gases,  and  is  not 
often  used  above  that  elevation.  The  expedient,  though,  in  one  sense  is 
quite  old;  because,  for  several  decades,  column  feet  of  trestles  and  elevated 
railroads  have  been  protected  by  enclosure  in  the  concrete  of  pedestal  tops. 

In  order  to  make  such  protection  truly  effective,  the  concrete  should  be 
water-proof.  This  result  can  be  accompUshed  in  a  number  of  ways. 
A  water-proofing  membrane  gives  the  most  certain  results;  but  in  niany 
instances  it  will  be  best  to  adopt  a  rich  mixture  and  to  add  to  the  cement 
some  five  or  ten  per  cent  of  its  volume  of  hydrated  hme.  This  matter  of 
water-proofing  is  treated  at  length  in  Chapter  XLIII. 

As  concrete  is  heavy,  its  use  for  a  metal  protector  adds  materially  to 
the  dead  load  of  structure,  thus  necessitating  the  employment  of  more 
steel  to  sustain  it;  hence  it  behooves  one  to  make  ihc  coating  as  thin  as 
practi(;ablc— and  yet  not  too  thin,  because  very  thin  concrete  may  not 
afford  the  requisite  protection,  unless  it  be  placed  by  pneumatic  gun,  in 
which  case  it  is  termed  gunite. 


ECONOMICS   OF  METAL  PROTECTION  443 

GUNITE 

There  is  an  economic  question  involved  in  choosing  between  ordinary 
concrete  and  gunite  for  metal  protection,  the  former  being  cheaper  per 
cubic  unit  but  requiring  a  larger  volume  and,  consequently,  more  metal 
to  sustain  its  greater  weight.  The  gunite  is  much  more  dense  than  ordinary 
concrete,  and  hence  affords  better  protection  against  moisture.  In  order  to 
prevent  its  cracking  under  changes  of  temperature,  it  generally  requires 
coarse  wire  mesh  or  expanded  metal  to  hold  it  together.  It  adheres  so 
closely  to  structural  steel  that,  in  order  to  remove  it  after  it  has  fully  set 
and  hardened,  chiseling  is  necessary.  Gunite  should  be  at  least  one  inch 
in  thickness.  When  shot  horizontal^  or  vertically  upward  the  covering 
is  strong  and  uniform;  but,  when  shot  vertically  downward,  sand-pockets 
are  likely  to  form,  unless  the  operation  be  carefully  watched  and  all  improp- 
erly-cemented material  instantly  removed. 

Treatment  of  Steel  that  is  to  be  Encased  in  Concrete 

OR  Gunite 

In  most  cases,  sufficient  attention  is  not  paid  to  the  covering  of  metal 
which  is  to  be  buried  in  concrete;  because,  if  it  is  given  a  coat  or  two  or 
ordinary  paint,  the  concrete  may  adhere  to  the  said  paint  all  right,  but  the 
latter  may  eventually  separate  from  the  metal,  thus  loosening  the  whole 
protection  and  either  lessening  or  destroying  its  efficiency.  In  the  old  days, 
when  the  question  was  much  more  simple  than  it  is  now  (involving,  as  it 
did,  only  the  burying  of  anchor  bolts  or  anchor  metal  in  the  concrete),  the 
author  solved  it  for  his  work  by  giving  the  metal  a  coat  of  boiled  hnseed  oil 
at  the  shops,  and  by  scrubbing  it  off  at  site  just  before  placement.  That 
method  would  be  impracticable  today  on  account  of  the  large  amounts  of 
steel  to  be  protected;  hence  one  might  put  on  the  ordinary  shop  coat  of 
red-lead  paint  and  take  it  off  after  erection  by  means  of  a  sand  blast,  thus 
leaving  the  clean  metal  exposed  to  the  concrete  or  gunite. 

Toch  Brothers,  however,  claim  that  their  No.  1087A  "R.I.W. "  paint, 
which  contains  no  saponifiable  oil  and,  therefore,  avoids  all  chemical  action 
between  the  concrete  and  the  paint,  will  make  a  permanent  bond  between 
the  steel  and  the  concrete.  Some  other  manufacturers  make  similar  claims 
for  special  products  of  their  own. 

Protection  Against  Brine  Drippings 

One  of  the  most  destructive  agencies  in  respect  to  bridge  metal  is  brine 
drippings  from  refrigerator  cars;  and,  as  yet,  no  satisfactory  protection 
against  it  has  been  found.  The  metal  most  injured  is  that  in  the  top  flanges 
of  stringers  and  cross-girders;  but  the  webs  and  bottom  flanges  thereof  and 
the  buck  braces  suffer  also  more  or  less.  Of  course,  the  ideal  method  of  pro- 
tection would  be  to  catch  the  drippings  in  receptacles  on  the  cars  and  thus 


444  ECONOMICS   OF  BRIDGEWORK  Chapter  XLII 

prevent  their  ever  reaching  the  bridges;  but  this  has  not  yet  been  done. 
It  is  a  matter  which  should  be  investigated  promptly ;  and,  if  an  effective 
remedy  for  the  trouble  be  found,  it  should  be  utiHzed  without  delaj^  by  aU 
railroads,  because  the  damage  done  by  the  drippings  is  not  confined  to  the 
floor-systems,  but  in  deck  truss-bridges  extends  also  to  the  upper  chords. 
The  total  value  of  the  annual  damage  to  all  the  steel  bridges  of  North  Amer- 
ica by  brine  drippings  must  amount  to  a  goodly  sum. 

The  railroads  are  now  struggling  with  the  owners  of  the  refrigerator- 
car  lines  in  an  endeavor  to  force  them  to  lead  the  brine  to  one  side  so  far 
that  it  will  not  drip  on  the  track  rails  and  their  fastenings;  but  nothing  of 
any  account  is  being  done  to  protect  steel  bridges  with  open  timber  decks, 
excepting  sometimes  to  cover  each  stringer  and  each  floor-beam  with  a 
wide  plank  or  to  daub  thickly,  the  top  surface  of  the  endangered  metal 
with  some  paint  or  other  compound  that  has  no  chemical  affinity  for  the 
brine. 

Protection  Against  Locomotive  Gases 

Another  deadly  agent  of  destruction  to  steel  bridges  is  the  gas  from 
steam  locomotives,  especially  when  they  pass  beneath  the  structure,  in 
which  case  the  gas  collects  in  semi-enclosed  spaces  where  it  remains  and 
steadily  attacks  first  the  paint  and  then  the  steel  beneath. 

As  before  mentioned,  the  surest  method  of  protection  against  such 
attack  is  to  enclose  the  entire  metalwork  below  the  elevation  of  track- 
rails  in  concrete  or  gunite.  Another  method  is  to  use  special  paint  beneath 
the  floor  and  to  hang  wooden  or  sheet-iron  protecting  platforms  close  to 
the  deck.  If  the  tops  of  the  smoke-stacks  of  the  locomotives  come  very 
near  to  the  floor  of  the  bridge  above,  especially  where  there  is  a  heavy 
up-grade,  cinders  are  driven  out  of  the  stacks  at  high  velocity,  combined 
with  smoke  and  steam,  thus  forming  the  most  effective  possible  kind  of 
blast  for  cutting  first  the  protection  and  then  the  steelwork  itself. 

Causes  of  Paint  Deterioration 

The  main  causes  for  deterioration  of  bridge  paint,  as  stated  by  the 
late  Mr.  Houston  Lowe,  are  as  follows: 

L  Water.     (Dissolution.) 

2.  Action  of  light  and  heat. .    (Chemical  and  physical  change.) 

3.  Chemical  action  between  pigment  and  binder.     (Disintegration.) 

4.  Abrasion  or  mechanical  injury.     (Motion.) 

5.  Action  of  deleterious  gases.     (Foul  air.) 

It  is  impracticable  to  keep  water  away  from  a  bridge,  but  the  design 
can  be  so  made  that  there  are  no  pockets  to  hold  it,  in  which  case  it  quickly 
runs  off  and  (evaporates. 

The  deleterious  action  of  light  and  heat  can  best  be  combated  by  a 
proper  choice  of  color  for  the  finishing  coat. 


ECONOMICS   OF  METAL   PROTECTION  445 

Disintegration  by  reason  of  chemical  action  between  pigment  and 
binder  is  a  matter  for  the  paint-manufacturers'  chemists  to  take  care  of; 
and  this  has  already  been  done  by  all  of  the  first-class  companies  with 
more  or  less  success. 

Abrasion  of  bridge  paint,  except  by  the  before-mentioned  cinder  blast 
from  steam  locomotives,  is  something  which  should  seldom  occur,  because 
nothing  should  be  allowed  to  strike  the  metalwork  of  a  bridge  hard  enough 
to  disturb  the  paint  thereon. 

In  respect  to  the  action  of  deleterious  gases,  that  question  has  already 
been  discussed  at  some  length  herein. 

How  TO  Care  for  Incipient  Failure  of  Paint 

As  all  bridges  should  be  submitted  to  careful  inspection  at  short 
intervals  of  time,  any  incipient  failure  of  paint  should  be  quickly  dis- 
covered. If  the  failure  pertains  to  the  field  coats  only,  it  will  suffice  to 
cover  the  defective  parts  with  a  layer  or  two  of  the  final  coating;  but,  if 
it  extends  into  the  shop  coat,  the  spot  affected  should  be  covered  with  red- 
lead  paint  of  best  quality,  and  afterwards,  for  the  sake  of  appearance,  re- 
covered with  some  of  the  finishing-coat  paint.  If  the  metal  is  exposed  and 
rusted,  which  will  not  occur  if  the  structure  is  properly  examined  at  inter- 
vals of  time  not  too  great,  some  scraping  will  be  necessary  before  the  red- 
lead  paint  is  applied. 

By  careful  attention  of  this  kind  the  life  of  the  paint  can  readily  be 
extended  from  twenty-five  to  fifty  per  cent,  as  compared  with  what  it  would 
be  without  such  attention. 

Determination  of  Time  for  Repainting 

When  the  partial  failures  begin  to  come  so  rapidly  that  the  retouching 
process  is  expensive  and  troublesome,  and  especially  when  the  attacks 
appear  to  be  liable  to  reach  the  metal  through  the  shop  coat,  it  is  about 
time  to  give  the  structure  a  thorough  cleaning  and  one  or  (better)  two  coats 
of  paint.  The  psychological  time  for  doing  this  can  only  be  determined  by 
an  experienced  bridge  man — preferably  the  Superintendent  of  Structures 
of  the  railroad,  state,  county,  or  municipality. 

Cleaning  ob'  Metalwork  Preparatory  to  Applying  New  Field 

Coats 

The  cleaning  of  the  metalwork,  if  it  has  been  properly  cared  for,  will 
not  prove  to  be  a  serious  business;  but,  otherwise,  it  will  involve  a  rather 
drastic  operation.  If  possible,  the  shop  coat  of  red  lead  should  not  be 
disturbed,  but  should  be  effectively  re-covered.  In  places  the  torch  may 
have  to  be  used;  but,  as  it  cuts  to  the  quick,  its  use  should  be  avoided 
whenever  practicable.     Similarly,  the  sand-blast  should  not  be  adopted, 


446  ECONOMICS   OF   BRIDGEWORK  Chapter  XLII 

unless  actual  rusting  has  started,  for  it  eats  into  the  metal;  and  some  good 
authorities  claim  that  where  it  is  employed  the  paint  will  not  adhere  as 
long  as  it  will  where  hand  cleaning  alone  has  been  adopted.  The  use  of  the 
sand  blast  deposits  a  lot  of  sand  in  numerous  corners  and  pockets  of  the 
metalwork;  and  it  should  all  be  carefully  brushed  therefrom  before  any 
painting  is  done. 

Application  of  Paint  after  Cleaning 

The  following  suggestions  concerning  field  painting,  if  followed,  should 
lead  to  economic  results  in  maintenance  of  bridges: 

First.  Avoid  both  cleaning  and  painting  in  wet  or  very  cold  weather. 
A  few  months'  delay  will  seldom  do  any  real  harm  to  the  metal  or  even  to 
the  priming  coat,  unless,  perchance,  the  bridge  has  been  neglected  to  the 
extent  of  actually  permitting  rusting  to  start. 

Second.  Never  do  much  cleaning  ahead  of  the  painting,  because  a 
spell  of  bad  weather  may  come  on  and  last  so  long  that  such  cleaning  wiU 
have  to  be  repeated.  It  is  not  only  the  extra  expense  of  doing  the  cleaning 
twice  which  is  uneconomic,  but  also  the  possible  injury  to  the  exposed  metal 
from  rusting  and  pitting. 

Third.  Provide  large  and  safe  platforms  for  both  cleaners  and  painters. 
It  is  true  that  these  may  be  expensive  in  both  first-cost  and  handhng,  but 
their  use  will  enable  the  workmen  to  do  a  much  greater  amount  of  work  per 
diem — and  better  work — than  if  they  were  not  effectively,  safely,  and  com- 
fortably supported.  Again,  there  is  to  be  considered  the  reduced  danger 
to  the  lives  of  the  workmen;  and  as  a  killed  employee  generally  costs  the 
company  $5,000,  and  an  injured  one  whatever  amount  he  can  persuade  the 
company  to  give  him  or  the  court  to  award,  it  is  certainly  economical  as 
well  as  humanitarian  to  reduce  the  danger  to  a  minimum. 

Fourth.  Give  the  first  field  coat  a  chance  to  dry  thoroughly  before 
applying  the  next  one.  In  a  long  structure  or  a  large  one,  requiring  weeks 
to  clean  and  paint,  this  restriction  will  work  no  economic  hardship;  but 
in  a  short  bridge  it  will,  often  necessitating  the  moving  of  the  painting 
gang  to  another  structure  and  returning  later  to  apply  the  second  coat. 

Fifth.  When  the  amount  of  cleaning  and  painting  is  large,  it  will  be 
economic  to ,  divide  the  gang  permanently  into  groups  of  cleaners  and 
painters;  but  when  the  bridges  are  small,  or  when  the  total  amount  of  work 
is  not  large,  ah  the  workmen  should  be  trained  so  as  to  become  proficient 
in  both  of  these  kinds  of  labor. 

Factors  that  Affect  Results  in  Painting 

As  stated  by  Mr.  Houston  Lowe;,  the  ])rin('ipal  factors  that  affect  results 
in  painting  an^  as  follows: 

1.  Lo(tation  of  the  structure,  for  example,  seaboard  or  inland. 

2.  Kind  and  condition  of  the  surface. 


ECONOMICS   OF   METAL   PROTECTION  447 

3.  Quality  of  the  paint  and  its  temperature. 

4.  Workmanship  of  the  painter. 

5.  Number  of  coats  appHed  and  their  sequence. 

6.  Time  allowed  to  elapse  between  coats. 

7.  Atmospheric  conditions  when  painting  is  done. 

By  giving  all  these  factors  due  consideration  when  handling  a  job  of 
bridge  painting,  and  by  striving  in  every  way  to  accommodate  the  work  in 
the  best  manner  possible  to  the  governing  conditions,  one  can  often  effect 
a  decided  economy. 

Economic  Observations  Concerning  Painting  in  General 

The  price  of  paint  is  a  matter  which  seldom  needs  much  consideration 
from  the  economic  standpoint,  unless  when  debating  on  the  choice  of  two 
or  three  kinds  of  nearly  equal  quality;  because  painting  is  so  much  more 
expensive  than  the  paint  itself  that  a  very  little  extra  hfe  of  the  coatings 
will  out-weigh  in  economic  importance  a  large  difference  in  the  cost  of  the 
material.  Generally,  one  should  determine  what  kinds  of  paint  would 
probably  be  the  best  for  any  job,  then  pay  for  them  whatever  is  necessary, 
unless  it  should  occur  that  the  seller  is  extortionate  in  his  demands,  which 
is  not  likely  to  be  the  case  when  dealing  with  first-class  business  men. 

It  does  not  pay  to  dicker  about  the  price  of  paint,  because  the  manu- 
facturer is  accustomed  to  ''cutting  his  coat  according  to  his  cloth."  The 
author  remembers  a  glaring  case  of  this  reprehensible  trick  that  occurred  in 
the  nineties.  He  had  been  using  very  satisfactorily  a  certain  magnetic- 
iron-oxide  paint  that  was  not  expensive,  and  recommended  it  to  a  contract- 
or-friend of  his  for  an  elevated  railroad  line.  Some  three  years  later  the 
paint  agent  dropped  into  the  author's  office  and  asked  him  to  specify  the 
brand  in  question  for  a  large  piece  of  work  then  about  to  be  let.  The 
request  was  refused — much  to  the  surprise  of  the  agent,  who  exclaimed  ''is 
not  our  paint  that  you  used  on  the  Blank  City  train-shed  giving  good  service 
after  four  years  of  use? "  The  reply  was:  "Yes;  but  how  about  the  con- 
dition of  your  paint  on  the  elevated  railroad  in  the  same  locality — is  it  not 
already  going  to  pieces  with  only  two  years'  service?"  In  answer  to  this 
question  the  agent  had  to  explain  that  the  Contractor  had  jewed  down  the 
price  and,  therefore,  the  paint  had  to  be  adulterated  in  order  to  meet  the 
cut.  Thereupon  the  author  refused  to  have  any  more  dealings  with  such  a 
dishonest  manufacturing  company,  and  never  again  adopted  the  said 
paint  on  any  of  his  metalwork. 

A  layer  of  good  paint  is  about  three  times  as  thick  as  a  layer  of  the  lin- 
seed oil  in  which  it  is  mixed,  and  the  increase  in  thickness  cf  the  former  is 
in  direct  proportion  to  the  fineness  of  the  pigment;  hence  it  is  economic 
to  have  the  said  pigment  ground  as  fine  as  possible,  for  it  is  a  fact  that,  with 
the  same  weight  of  oil  and  the  same  weight  of  pigment,  the  greater  the 


448  ECONOMICS   OF   BRIDGEWORK  Chapter  XLII 

volume  of  the  latter — i.e.,  the  finer  it  is  ground — the  more  slowly  will 
the  paint  dry  and  the  longer  will  it  endure. 

The  correct  and  economic  theory  of  metal  painting  is  that  the  paint 
used  for  the  priming  coat  should  be  of  a  preservative  nature,  i.e.,  of  such  a 
character  that  it  will  not  only  possess  the  power  of  inhibiting  the  corrosion 
of  the  metal  but  also  that  of  absolutely  excluding  air  and  moisture  there- 
from, and  that  the  other  coats  should  be  of  a  protective  nature,  i.e.,  that 
they  will  protect  the  priming  coat  from  the  deleterious  action  of  rain,  sun- 
shine, and  all  other  deteriorating  agents. 

In  respect  to  the  character  of  the  pigments  for  the  finishing  coats,  it  is 
important  that  they  be  both  chemically  and  physically  inert,  that  they  be 
ground  very  fine,  and  that  they  have  an  affinity  for  linseed  oil.  It  is  a 
matter  of  minor  importance  whether  the  pigment  be  graphite,  lampblack, 
charcoal,  oxide  of  iron,  or  what  not,  as  far  as  durability  is  concerned. 
Where  only  three  coats  of  paint  are  to  be  used,  it  is  often  advantageous  to 
employ  for  the  middle  one  a  direct  mixture  of  the  priming  and  the  finishing 
paints. 

The  character  of  the  brush  used  is  an  important  element  in  painting; 
for  it  is  possible  to  ruin  a  coat  of  good  paint  by  applying  it  with  a  broad, 
thin,  flat  brush.  Instead,  the  paint  should  be  well  rubbed  into  the  surface 
with  a  stout,  full,  round,  bristle  brush.  "Less  paint  and  more  painting" 
should  be  the  slogan  for  every  painter  who  desires  to  do  good  work. 

A  temperature  of  about  70°  F.,  combined  with  an  atmosphere  free 
from  moisture,  makes  the  ideal  condition  for  both  the  applying  and  the 
drying  of  paint.  The  matter  of  humidity  is  of  even  greater  importance 
than  that  of  temperature;  because  nothing  retards  drying  more  than 
dampness  and  darkness. 

For  places  that  are  badly  ventilated,  where  sunshine  does  not  reach, 
and  that  are  damp  or  at  times  filled  with  steam  or  locomotive  gases,  it  is 
economic  to  use  a  special  kind  of  coating,  preferably  a  varnish  or  resin  paint 
so  composed  that  it  will  dry  rapidly. 

This  dissertation  on  paint  and  painting  could  be  carried  on  almost  indef- 
initely; but,  if  it  were,  the  author  might  properly  be  open  to  criticism  for 
departing  from  his  subject  of  economics.  It  is  possible  that,  even  as  it  is, 
some  of  the  readers  of  this  chapter  will  accuse  him  of  that  fault.  If  so,  he 
would  reply  that  anything  which  treats  of  how  to  prolong  the  life  of  bridge 
paint  or  to  protect  the  metal  effectively  against  corrosion  is  directly  in  the 
line  of  true  economics. 

Summarizing  in  a  very  few  words  all  that  has  been  said  herein  upon  the 
subject  of  "Economics  of  Metal  Protection,"  it  may  be  stated  that  it 
is  always  truly  economic  to  use  the  best  protective  agencies  procurable, 
irrespective  of  their  cost,  and  to  spend  without  hesitation  all  the  money 
requisite  for  taking  the  very  best  of  care  of  the  metalwoi-k  in  all  first-class 
railway  and  highway  bridges — or,  for  that  matter,  in  any  other  bridges 
that  arc  worth  saving  from  speedy  destruction. 


CHAPTER  XLIII 

Economics  of  Water-proofing 

The  economics  of  water-proofing  solid-floor  bridges  might  properly  be 
considered  in  the  chapter  on  "Economics  of  Maintenance  and  Repairs," 
or  in  that  of  "Economics  of  Metal  Protection";  but  the  subject  is  one  of 
such  importance  that  it  truly  merits  special  treatment  in  an  independent 
chapter. 

Very  few  engineers  are  sufficiently  conversant  with  the  water-proofing  of 
bridges  to  permit  of  their  writing  authoritatively  upon  the  subject  of  its 
economics,  and  the  author's  experience  therein  certainly  has  not  been 
very  extensive;  hence  he  deems  himself  exceedingly  fortunate  in  having 
secured  the  aid  of  Mr.  J.  B.  W.  Gardiner,  President  of  Gardiner  and  Lewis, 
Inc.,  of  New  York  City,  who  has  made  a  special  study  of  the  subject, 
extending  over  several  years,  and  who  has  very  kindly  prepared  for  him 
the  substance  of  the  following  dissertation: 

The  economics  of  water-proofing  means  this:  Is  or  is  not  water-proof- 
ing worth  while  financially?  does  the  effect  produced  or  the  protection 
afforded  the  structure  by  water-proofing  the  floor  justify  the  expenditure 
involved?  It  must  be  assumed  at  the  outset  that  the  same  care  has  been 
taken  with  the  water-proofing  as  is  taken  ordinarily  with  the  steel  or  other 
structural  material,  i.e.,  that  the  bridge  was  designed  to  be  water-proofed, 
that  a  careful  selection  of  materials  was  made,  and  that  those  materials 
were  installed  by  men  skilled  in  that  particular  trade,  or  at  least  were 
placed  under  careful  supervision.  These  conditions  are  no  more  stringent 
or  unreasonable  than  those  which  apply  to  the  design,  fabrication,  and 
placing  of  other  materials  that  go  into  the  structure.  The  initiatory  pre- 
sumption is,  therefore,  entirely  proper. 

Whether  water-proofing  as  applied  to  bridge  floors  is  a  profitable  invest- 
ment depends  on  several  factors.     These  are : 

a.  The  proportionate  original  cost  of  the  water-proofed  bridge  as 
compared  with  the  total  cost  of  the  bridge  without  water- 
proofing. 

6.  The  probable  life  of  the  water-proofing  and  the  probable  cost  of 
its  renewal. 

c.     Its  effect  on  the  life  of  the  structure  itself  and  on  the  cost  of 
maintenance  and  repairs. 
d49 


450  ECONOMICS   OF   BRIDGEWORK  Chapter  XLIII 

The  original  cost  of  water-proofing  is  a  function  of  a  number  of  different 
factors.  The  cost  of  the  material  itself  delivered  at  site,  that  of  the  direct 
labor  involved  in  placing  it,  the  cost  of  such  provisions  as  are  made  for 
flashing  along  the  hnes  of  tenniiiation  of  the  water-proofing,  the  cost  of 
the  protective  or  armor  coat,  the  additional  depth  of  flooring  and  the 
greater  strength  that  must  be  provided  in  steel  bridges  to  carry  the  dead 
load  of  the  water-proofing  and  its  protection,  and  the  accessibihtj'  of  the 
site  of  the  work,  are  all  considerations  that  influence  the  solution  of  this 
question  of  economics.  It  is  readily  seen  that  the  cost  of  water-proofing 
must  be  a  fundamentally  variable  factor,  as  weU  as  one  which  fluctuates 
with  the  building-material  market.  Moreover,  the  cost  per  square  foot  is 
usually  greater  in  the  case  of  steel  bridges  than  when  the  protection  is 
appHed  to  concrete  viaducts;  because,  in  the  latter,  the  increase  in  the 
dead  load  does  not  materially  affect  the  design,  and  also  because  in  con- 
crete bridges  the  protection  coat  is  usually  a  part  of  the  paving-floor  system 
(except  in  bridges  of  the  sohd-spandrel,  earth-filled  type),  and  hence 
involves  no  additional  cost.  At  present-day  prices,  however,  a  cost  of  40 
cents  per  square  foot  for  water-proofing  steel  bridges  or  35  cents  per  square 
foot  for  water-proofing  concrete  bridges  is  a  fair  average. 

The  relative  cost,  i.e.,  the  cost  of  the  water-proofing  as  compared  with 
the  total  cost  of  the  structure,  is  also  variable.  In  the  case  of  unique  steel 
bridges,  such  as  the  Hell  Gate  Arch  or  the  Quebec  Cantilever  Bridge  over 
the  St.  Lawrence  River,  or  in  unusual  concrete  bridges,  such  as  the  Tunk- 
hannock  Creek  Viaduct  on  the  D.  L.  &  W.  R.  R.,  this  percentage  cost  is 
abnormally  low,  because  of  the  extremely  high  cost  of  those  structures  per 
square  foot  of  floor  area.  But  such  structures  as  those  are  so  unusual  that 
we  may  ignore  them  in  our  cost  considerations,  and  base  our  results  on  the 
more  common  types  of  bridges. 

Data  gathered  from  several  eastern  railroads  show  that,  of  the  total 
cost  of  a  steel  bridge,  four  per  cent  is  properly  chai-geable  to  water-proofing. 
In  computing  this  figure  various  standard  types  of  bridges  were  considered 
i.e.,  concrete-filled  trough-floors,  plate-girders  wdth  transverse  I-beam  floors, 
longitudinal  I-beam  floors  with  steel-plate,  and  deck-girder  bridges.  Cost 
data  were  also  gathered  for  different  periods — before,  during,  and  after  the 
war — and  the  results  were  averaged.  It  might  be  remarked  in  passing  that 
the  advance  in  water-proofing  costs  has  not  kept  pace  with  the  advance  in 
other  elements  of  construction.  For  example,  in  1914  the  steel  in  a  certain 
bridge  cost  S73  per  ton  erected  and  the  water-proofing  28  cents  per  square 
foot.  In  1917-1918  the  steel  in  a  bridge  of  exactly  the  same  type  cost  $143 
per  ton  erected,  while  the  water-proofing  cost  but  35^  cents  per  scjuarc  foot. 
Thus,  although  the  steel  increased  in  cost  ninety-six  per  cent,  the  water- 
proofing inci-eased  only  twenty-seven  per  cent.  When  it  is  stated,  there- 
fore, that  the  cost  of  water-pi'oofing  averages  four  per  cent  of  the  cost 
of  the  structure,  we  are  takirig  a  figui'(»  which  is  really  extreme  and  which 
we  may  safely  assume  will  not  be  exceeded,  except  in  isolated  and  very 


ECONOMICS   OF   WATER-PROOFING  451 

extreme  cases.  To  look  at  this  percentage  in  another  Hght,  the  interest 
on  the  cost  of  a  bridge  for  one  year  at  four  per  cent  will  pay  for  the  water- 
proofing. 

In  concrete  bridges  the  relation  between  water-proofing  costs  and  total 
costs  is  apparently  a  variable  with  wide  limits,  because  the  character  of  the 
pier-work  exercises  such  a  great  influence  on  the  latter  figure.  As  a  matter 
of  fact,  however,  for  certain  types  of  bridges  this  relation  is  surprisingly 
uniform;  but  distinction  must  be  made  between  two  classes  of  concrete 
bridges,  in  order  to  arrive  at  the  proper  ratio.  This  is  because  of  the  cost 
of  the  protection  or  armor  coat  placed  on  the  water-proofing.  Such  pro- 
tection is  always  adopted  for  concrete  railroad  bridges  of  whatever  type, 
and  for  earth-filled,  solid-spandrel  highway-bridges.  These  two  then  may 
be  considered  together.  On  flat-slab  highway  bridges,  the  protection  coat 
is  frequently  omitted;  and,  if  used,  it  is  little  more  than  a  grouting  course 
under  the  paving,  which  might  be  required  even  if  the  bridge  were  not 
water-proofed.     This  type  of  bridge  constitutes  the  second  class. 

In  the  first  class  the  cost  of  water-proofing  bears  about  the  same  relation 
to  the  total  cost  as  was  found  in  the  case  of  steel  bridges — i.e.,  an  average 
of  four  per  cent.  Isolated  cases  were  encountered  in  railroad  viaducts 
where  the  cost  of  water-proofing  ran  up  to  eight  per  cent;  but  this  was 
exceptional,  the  usual  cost  being  well  under  five  per  cent. 

On  flat-slab  highway-bridges  remarkable  uniformity  in  relative  costs 
was  found.  Ninety  per  cent  of  the  cost  figures  which  were  analyzed  showed 
the  expense  of  water-proofing  to  be  between  one  and  a  half  and  two  per 
cent,  and  only  a  single  bridge  showed  a  greater  cost.  This  last  figure, 
therefore,  may  safely  be  taken  as  a  fair  average.  Thus  in  all  bridges, 
steel  or  concrete,  except  flat-slab-floor  highway-bridges,  the  water-proofing 
cost  is  four  per  cent  of  the  total,  while  in  flat-slab-floor  structures  it  is  two 
per  cent  thereof. 

The  only  element  of  cost  which  has  not  been  considered  is  that  of  the 
interest  on  the  investment;  but  this  will  not  change  the  ratios  which  have 
already  been  arrived  at,  since  the  rate  of  increase  in  the  cost  of  water- 
proofing through  the  addition  of  interest  charges  is,  of  course,  identical  with 
the  rate  of  increase  in  the  value  of  what  the  water-proofing  is  to  protect, 
hence  this  element  of  cost  may  be  ignored. 

Probable  Life  of  Water-proofing 

By  the  probable  fife  of  water-proofing  is  meant,  of  course,  its  effective 
hfe, — the  length  of  time  it  will  continue  to  exercise  its  water-excluding 
function.  If  a  bridge  has  been  properly  designed  with  respect  to  water- 
proofing details,  and  if  the  water-proofing  has  been  properly  placed  it  will 
fail,  if  at  all,  from  one  or  both  of  two  causes, — a  break  in  the  continuity  of 
the  water-proofing  envelope  by  rupture  or  otherwise,  and  the  deterioration 
of  the  water-proofing  material  itself  by  oxidation  or  rotting.     The  shock  of 


452  ECONOMICS   OF   BRIDGEWORK  Chapter  XLIII 

impact  when  a  locomotive  first  passes  on  a  bridge,  the  grinding  wrench  when 
brakes  are  appHed  while  it  is  on  the  structure,  the  vibration  of  any  steel 
construction  caused  by  the  moving  load,  the  deflection  and  reverse  bending 
on  continuous-span  steel-bridges,  the  changes  in  volume  incident  to  tem- 
perature variations — all'  these  place  very  severe  but  indefinite  stresses  on 
the  water-proofing  blanket.  At  the  same  time,  an  engineer,  knowing  these 
conditions,  can  select  a  material,  the  physical  properties  of  which  will 
generally  meet  them.  Materials  which  are  brittle  at  low  temperatures 
should  receive  scant  consideration,  because  of  the  probabihty  of  their  being 
fractured  by  vibration  in  cold  weather.  Materials  which  are  very  soft  at 
high  temperatures  should  likewise  be  regarded  with  suspicion,  because  they 
cannot  be  held  on  vertical  or  steeply-inclined  surfaces.  Finall}^,  a  material 
should  be  selected  all  parts  of  which  are  flexible  and  elastic,  so  that  they 
will  yield  rather  than  break  under  the  conditions  mentioned.  To  put  it 
briefly,  the  water-proofing,  in  so  far  as  physical  requirements  are  concerned, 
should  be  selected  on  the  basis  of  its  plasticity  or  flexibility  at  all  tempera- 
tures and  its  small  factor  of  susceptibihty  to  temperature  changes.  As  to 
the  deterioration  of  water-proofing,  that  is  almost  entirely  a  chemical 
matter.  The  exclusion  of  all  materials  that  are  affected  by  water,  whether 
or  not  the  water  carries  acids  or  alkahes,  such  as  the  hgno-cellulose  com- 
pounds (jute  or  burlap)  and  the  felts  in  which  tapioca  is  the  binding  medium 
(asbestos  felt),  the  non-employment  of  those  that  are  physically  unstable, 
such  as  most  of  the  artificially  compounded  asphalts  and  asphalts  contain- 
ing organic  matter,  and  the  selection  of  a  material  which  has  to  a  large 
degree  been  pre-aged  or  pre-oxidized  will  assure  long  fife  for  the  protection. 
Indeed,  water-proofing  materials  (asphaltic)  placed  in  2500  b.c.  have 
lately  been  found  to  be  still  in  good  serviceable  condition.  A  discussion  of 
the  various  materials  sold  for  bridge  water-proofing  is  a  compKcated  one 
and  very  technical.  It  is  relevant  to  the  subject  of  this  chapter  only  in  so 
far  as  it  may  point  out  the  answer  to  the  questions  that  have  been  raised. 
It  is  sufficient  to  say,  however,  that  if  a  selection  of  materials  is  made  with 
regard  to  the  known  conditions  which  must  be  met,  rather  than  on  the 
basis  of  initial  cost,  a  life  of  at  least  25  years  may  reasonably  be  antici- 
pated, with  the  probability  that  this  figure  will  be  greatly  increased. 

It  is  obvious  that,  if  water-proofing  a  bridge  floor  is  economically  wise, 
the  resultant  value  of  the  protection  afforded  to  the  structure  thereby  must 
exceed  the  cost  thereof.  That  the  said  value  does  exceed  the  cost  may  be  a 
difficult  proposition  to  establish  by  definite  figures.  As  far  as  is  known,  no 
data  exist  concerning  the  amount  of  the  damage  caused  by  lack  of  water- 
proofing. All  that  can  be  done  with  this  question  is  to  indicate  the  agents 
which  attack  l)ridge  floors  and  tlu^  effcn-t  of  water-jiroofing  in  warding  off 
such  attacks,  leaving  it  to  the  judgment  of  the  intlividual  to  decide  whether 
the  probabilities  in  the  case  justify  the  expense  which  water-proofing 
involves. 

For  convenience  in  treatment,  the  effect  of  water  on  steel  alone  will  be 


ECONOMICS   OF   WATEK-PROOFING  453 

considered  in  connection  with  steel  bridges,  the  effect  thereof  on  the  con- 
crete floor  of  such  structures  being  discussed  in  connection  with  concrete 
viaducts.  The  primary  function  of  water-proofing  on  steel  bridges  is  to 
furnish  protection  to  those  steel  members  which,  because  of  the  very  exist- 
ence of  the  sohd  floor,  are  not  accessible  for  ordinary  maintenance.  They 
cannot  be  painted  or  otherwise  guarded  from  moisture — as  they  are,  so 
must  they  remain.  On  railroad  structures  the  flow  of  water  to  the  drains  is 
seriously  interfered  with  by  the  ballast,  which,  to  some  extent,  acts  as  a  dam 
to  hold  the  water  on  the  surface  of  the  concrete  floor.  The  said  concrete 
floor  may  thus  become  saturated,  because  of  the  moisture  being  held  for  a 
considerable  time  against  the  steel — an  ideal  condition  for  destructive  cor- 
rosion. 

Brine-drip  from  refrigerator  cars  is  a  singularly  active  corrosive  which 
is  a  cause  of  trouble  and  annoyance  to  bridge  engineers  everywhere,  its 
effect  being  very  frequently  seen  on  the  top  flanges  of  stringers  and  floor 
beams,  where  it  is  extremely  destructive.  Not  only  are  these  affected,  but 
also  in  half-through,  plate-girder  bridges  those  portions  of  the  webs  of  the 
girders  which  are  covered  by  the  concrete  are  also  subject  to  corrosion,  as 
the  joints  where  the  concrete  meets  the  steel  invariably  open  sufficiently  to 
allow  water  to  enter. 

It  is  unnecessary,  though,  to  dilate  further  on  the  action  of  either  atmos- 
pheric water  or  brine-drip  on  steel.  The  facts  are  well  known  and  univer- 
sally recognized,  and  it  is  conceded  that  many  bridges  have  been  seriously 
damaged  by  rust,  even  to  the  extent  of  having  to  be  replaced.  This  deteri- 
oration can  be  prevented  on  the  exposed  metal  by  painting;  but  the  only 
protection  that  can  be  given  to  those  members  which  are  not  exposed  is 
water-proofing.  The  actual  money  damage  resulting  from  failure  to  water- 
proof cannot,  for  lack  of  dependable  data,  be  definitely  stated.  Certain 
it  is,  however,  that,  if  a  steel  bridge  is  left  unpainted  long  enough,  the 
sectional  areas  of  the  metal  will  be  so  reduced  that  the  structure  will 
become  unfit  for  use  and  ready  for  the  scrap  heap.  And  if  this  is  true  of 
the  exposed  members  from  which  the  water  dries  out  quickly,  how  much 
more  true  is  it  of  those  members  which  are  subjected  to  a  greatly  aggra- 
vated condition!  At  just  what  period  inaccessible  and  unprotected  steel 
will  become  unsafe  no  one  can  say;  but  the  fact  that  so  many  and  such 
important  members  cannot  be  inspected  so  as  to  determine  their  condi- 
tion would  appear  to  impose  upon  an  engineer,  from  the  standpoints  of 
both  public  safety  and  economy  to  his  client,  the  duty  of  protecting  the 
metal  by  efficient  water-proofing.  With  increasing  live  loads,  it  is  all  the 
more  necessary  to  maintain  the  full  strength  of  the  steelwork,  and  not  to 
allow  of  its  weakening  by  preventable  deterioration. 

From  the  foregoing  it  is  evident  that  water-proofing  is  a  necessity  for 
bridges  which  contain  structural  steel  embedded  in  the  concrete  of  the 
floor,  and  for  those  having  members  encased  in  concrete  or  gunite.  Failure 
to  follow  this  practise  has  caused  loss  in  some  instances,  the  encased 


454  ECONOMICS   OF   BRIDGEWORK  Ch.^pter  XLIII 

members  being  seriously  weakened,  and  the  encasement  being  split  off  by 
rust.  It  is  not  so  important  when  the  concrete  slab  merely  rests  on  the 
tops  of  the  stringers  without  encasing  them;  for  the  destructive  effects 
are  then  hmited  almost  entirely  to  the  slab  itself  and  to  the  tops  of  the 
stringer  flanges. 

The  question  as  to  whether  reinforced-concrete  viaducts  should  be 
water-proofed  is  somewhat  more  complicated  than  that  for  steel  bridges, 
owing  to  the  fact  that  there  is  not  the  same  concurrence  of  opinion  as  to 
the  injurious  effect  of  water  on  the  structure.  It  may  be  stated,  though, 
that  the  water-proofing  of  concrete  viaducts  has  lately  become  a  conmion 
practice  with  the  railroads  of  this  country  and  with  many  of  the  private 
consulting  engineers,  as  well  as  with  a  number  of  state,  countj^,  and  muni- 
cipal officials.  Certainly,  those  engineers  who  include  water-proofing  in 
their  specifications  are  actuated  by  the  same  desire  to  produce  creditable 
work,  the  same  loyalty  to  the  interest  of  their  chents,  as  those  who  do 
not.  This  being  the  case,  on  what  theory  and  for  what  reasons  do  they 
consider  it  justifiable  to  make  this  addition  to  the  cost  of  the  structure? 
Just  lohy  should  a  reinforced-concrete  viaduct  be  water-proofed? 

That  there  is  virtue  in  water-proofing  a  flat  slab,  even  though  weU 
pitched  for  drainage,  is  shown  by  the  experience  of  the  country  with  con- 
crete roads.  It  cannot  be  denied  that  such  roads,  well  blanketed  with 
asphalt,  give  longer  and  better  service,  with  less  cracking  and  other  evi- 
dence of  disintegration,  than  those  not  so  blanketed.  While  this  is  partly 
due  to  the  fact  that  mechanical  wear  is  eliminated,  the  protection  of  the 
concrete  from  the  action  of  frost  and  freezing  water  is  an  important  factor. 
The  drainage  problem  on  a  road  is  much  more  simple  than  that  on  a 
bridge  floor.  The  standard  width  of  road  is  generally  but  18',  so  that  the 
area  to  be  drained  is  only  9'  wide — the  distance  from  the  crown  to  the 
curb.  The  areas  on  a  bridge  floor  are  generally  much  larger;  and  since 
the  water  must  be  conducted  to  small  down  spouts,  instead  of  to  an  open 
trench,  as  is  the  case  with  a  road,  the  problem  in  bridgework  exists  in  a 
much  more  aggravated  form.  If,  therefore,  it  is  found  that  water-proofing 
a  concrete  road  by  means  of  an  impervious  blanket  of  asphalt  protects  the 
road,  prevents  its  disintegration,  and  prolongs  its  life,  how  much  more 
urgent  is  the  need  for  water-proofing  a  bridge  floor? 

A  brief  analysis  of  the  more  important  of  the  disintegrating  effects  of 
water  penetrations  on  concrete  will  serve  to  bring  out  the  reasons  why 
from  an  economic  standpoint — i.e.,  from  the  standpoint  of  preservation 
and  consequent  reduction  in  both  annual-replacement  reserves  and  main- 
tenance charges, — the  water-proofing  of  concrete  bridges  is  profitable. 

Water  is  a  universal  solvent,  affecting,  of  course,  some  materials  more 
than  others.  Th(u-e  is  in  concrete  sonic  solulile  matter;  and,  if  water  be 
permitted  to  pass  completely  through,  such  soluble  n\atter  is  gradually 
removed  by  a  lea(^hiiig  process.  This  is  shown  by  the  fact  that  water, 
after  it  has  passed  through  concrcite,  will  invariably  give  alkaline  reaction, 


ECONOMICS   OF   WATER-PROOFING  455 

indicating  that  it  has  carried  away  some  of  the  hme  or  other  alkali  content 
of  the  cement.  Coupled  with  this  is  an  erosive  action  which,  while  shght, 
is  nevertheless  present.  Particularly  are  both  solvent  and  erosive  actions 
aggressive  at  the  construction  joints,  as  is  evidenced  by  the  excrescence  of 
magnesia  and  other  salts  on  the  under  surface  at  these  places.  This  is 
because  at  the  joints  there  is  almost  always  found  a  film  or  deposit  of 
laitance,  which  is  loose  in  texture,  non-coherent,  chalky,  and  very  porous. 
Water,  if  allowed  to  pass  through  the  concrete  at  the  said  joints,  will  both 
leach  and  erode  the  joint  walls  very  rapidly,  thus  exposing  the  reinforcing 
steel  to  the  air  with  consequent  corrosion,  and  opening  the  way  in  temper- 
ate and  cold  climates  to  the  disruptive  effect  of  frost.  The  result  of  these 
combined  actions  on  concrete  is  certainly  the  weakening  of  the  structure,  as 
well  as  the  making  ready  for  further  and  more  drastic  effects  of  water  dis- 
integration. 

In  climates  where  freezing  temperatures  prevail  in  winter,  there  are 
peculiarly  forceful  reasons  for  water-proofing  bridge  floors.  The  dis- 
ruptive force  of  freezing  water  is  one  of  the  most  destructive  agencies 
operating  against  masonry  of  whatever  nature,  whether  its  mass  be  mainly 
natural  or  artificial.  It  is  particularly  harmful  where  the  masonry  con- 
tains cracks,  however  small  or  shallow  they  may  be,  into  which  water  can 
penetrate  freely.  This  again  has  a  most  direct  bearing  on  concrete  bridge 
floors.  In  common  with  most  fiat-slab  constructions,  whether  the  slab 
rest  on  arches  or  beams,  bridge  floors  are  almost  certain  to  develop  cracks. 
They  may  be  merely  shrinkage  cracks  incident  to  the  setting  of  the  con- 
crete, and  hence  more  or  less  superficial,  or  they  may  be  expansion  cracks 
extending  through  the  full  depth  of  the  slab ;  but  the  ultimate  results  will 
be  practically  the  same.  If  only  surface  cracks  exist,  these  will  fill  with 
water,  which,  on  freezing,  will  break  down  the  surrounding  walls,  causing 
the  concrete  to  spall.  It  will  thus  be  weakened  along  the  line  of  the  crack, 
which  must  inevitably  be  deepened  with  each  repetition  of  the  process,  until 
the  injury  has  extended  through  the  entire  thickness  of  the  slab.  Further- 
more, since  the  concrete  has  been  weakened  along  this  line,  any  unusual 
stresses  incident  to  expansion,  or  other  force,  are  apt  to  spht  the  slab  at  the 
weakened  section.  ?■:  ■ 

Where  the  crack  extends  completely  through  the  slab,  the  action  is  still 
more  serious.  In  such  a  case,  the  same  frost  action  may  force  the  walls  of 
the  crack  apart  a  material  distance,  exposing  the  reinforcing  metal  to  unin- 
rupted  and  unavoidable  corrosion,  thus  weakening  the  entire  structure. 
If  electricity  be  present,  the  condition  will  be  aggravated  by  electrolysis, 
which  will  not  only  accelerate  the  corrosion  of  the  steel  but  also  will  soften 
the  concrete,  providing  it  be  moist  or  wet.  (See  Tech.  Paper,  No.  19, 
U.  S.  Bureau  of  Standards.)  If  electrolytic  action  does  occur,  the  concrete 
is  certain  to  be  split  away  from  the  reinforcing  material  by  the  mechanical 
pressure  of  the  forming  rust  scale,  which  pressure  has  been  recorded  as  high 
as  4,700  pounds  to  the  square  inch. 


456  ECONOMICS   OF   BRIDGEWORK  Chapter  XLIII 

Efficient,  well-planned  water-proofing  is  the  only  sure  preventive  of 
these  evils. 

As  provocative  of  cracks  in  concrete,  the  effect  of  moisture-changes 
merits  attention.  It  has  been  fully  demonstrated  by  some  most-carefully- 
conducted  tests  that  concrete  expands  in  volume  on  becoming  wet.  This 
fact  may  well  produce  cross  stresses  in  the  slab,  which  will  result  in  the 
cracking  of  the  surface.  If,  for  example,  we  have  a  floor  slab  10  inches 
thick,  and  if  sufficient  water  falls  upon  it  to  wet  it  to  a  depth  of  two  inches, 
the  upper  two  inches  will  have  a  tendency  to  swell  or  expand,  while  the 
lower  8  inches  will  remain  fixed.  Along  the  planes  separating  these  two, 
therefore,  there  will  be  produced  a  stress  which  no  amount  of  provision 
could  guard  against.  Should  this  cross  stress  produce  surface  fissures  or 
cracks,  the  way  is  opened  for  the  ultimate  disintegration  which  has  been 
mentioned. 

On  this  point,  Hool  &  Johnson,  in  their  "Concrete  Engineers'  Hand 
Book"  made  the  following  statement: 

"The  expansion  and  contraction  of  mortars  and  concretes,  subjected  to  variations 
of  temperature  and  moisture  conditions,  are  responsible  for  practically  all  failures  of 
these  materials  under  conditions  of  exposure  to  the  weather.  Either  temperature  effects 
or  moisture  effects  may  be  alone  operative,  or  both  effects  may  be  combined.  ...  In 
the  average  situation  the  introduction  of  dangerous  stresses  caused  by  a  tendency  to 
expand  or  contract  is  more  apt  to  be  due  to  moisture  changes  than  to  temperature 
changes,  because  the  volumetric  variations  in  the  latter  cases  are  less  marked." 

There  is  still  another  factor  entering  into  the  subject,  to  which  engineers 
generally  are  not  inclined  to  pay  sufficient  consideration,  largely  because 
it  is  one  which  is  not  directly  or  immediately  measurable  in  dollars  and 
cents,  viz.,  the  matter  of  appearance. 

There  is  no  concrete  structure  which  is  designed  for  a  greater  degree  of 
permanency  than  a  reinforced-concrete  viaduct.  It  is  almost  invariably 
an  important,  indeed  a  vital,  link  in  a  railway  or  a  national  or  state  high- 
way, the  line  of  which  does  not  change  in  a  generation;  and  it  is  usualty 
designed  to  carry  many  times  the  load  which  present  conditions  render 
requisite,  thus  making  improbable  the  necessity  for  renewal  by  reason  of 
changes  in  transportation  methods.  It  stands,  therefore,  through  many 
years  a  monument  to  the  man  who  designed  it,  as  well  as  an  indication  of 
the  progressive  spirit  of  the  community;  consequently,  both  from  the  stand- 
point of  the  designing  engineer  and  fi-om  that  of  the  community,  every 
reasonable  precaution  should  be  taken  to  preserve  the  appearance  of  what 
is  naturally  a  beautiful  structure. 

If  water  is  permitted  to  flow  freely  through  a  bridge  floor,  the  result  will 
invariably  be  the  excrescence  of  magnesia  and  other  salts,  which  appear  on 
the  surface  in  the  form  of  a  white  "bloom."  This  is  particularly  in  evi- 
dence at  the  constnu^tion  joints,  and  notably  at  the  joints  between  suc- 
cessive arch  ribs.  Notliing  is  more  disfiguring  to  a  concrete  bridge,  nothing 
is  more  indicative  of  careless  or  incomplete  work,  than  the  discoloration  of 


ECONOMICS   OF   WATER-PROOFING  457 

a  structure  due  to  the  action  of  water.  It  is  readily  guarded  against  at 
small  cost;  hence,  for  aesthetic  as  well  as  preservative  reasons,  water- 
proofing is  well  worth  while. 

This  consideration,  apparently  purely  aesthetic,  has,  paradoxical  as  it 
may  seem,  a  distinct  place  in  a  discussion  of  the  economics  of  bridge  water- 
proofing. Cities  and  towns  are  in  constant  competition  with  each  other 
for  new  industries.  Large  sums  of  money  are  spent  annually  by  these 
municipalities  or  their  3oards  of  Trade  in  advertising  their  advantages  as 
loci  for  manufacturing  enterprises.  Visible  evidences  of  a  spirit  of  progress 
in  the  community,  obvious  care  in  attention  to  details  of  appearances  of 
public  structures,  are  impressive  and  cannot  fail  to  attract  the  notice  of 
prospective  residents.  This  makes  for  the  wealth  and  progress  of  all  con- 
cerned. When  a  visitor's  first  impression  of  a  city  is  produced  by  seeing 
what  should  be  a  beautiful  monumental  construction  covered  with  the 
disfiguring  surface-blemishes  which  water-penetration  produces,  he  is  apt 
to  turn  to  a  competitor  whose  neglect  of  detail  is  not  so  marked ;  for  to  the 
layman — this  term  being  used  to  differentiate  from  the  engineer — such 
blemishes  mean  more  than  mere  surface  disfiguration,  because  they  convey 
the  impression  of  general  disintegration  and  eventual  failure,  and  reflect 
unfavorably  upon  the  community  or  the  owner  of  the  structure. 

It  is  not  contended  that  the  neglect  to  water-proof  a  concrete  bridge 
will  always  result  in  its  ultimate  destruction.  Many  bridges  which  are 
not  water-proofed  are  still  intact;  few  have  completely  failed.  But 
water-proofing  certainly  does  provide  a  measure  of  protection.  It  is,  in 
fact,  a  form  of  insurance.  The  cost  is  small — not  more  than  two  per  cent 
of  the  total — so  that  if  it  extends  the  life  of  a  bridge  only  a  year  or  two,  it  is 
worth  while,  since  the  prolonged  use  of  the  structure  is  almost  always  of 
greater  value  than  the  extra  cost  plus  compound  interest  thereon.  When, 
however,  the  protection  afforded  is  not  merely  for  a  year  or  two,  but  for 
a  great  many  years,  the  life  of  the  water-proofing  being  the  only  limit, 
and  even  that  being  capable  of  extension  by  renewals,  it  is  obvious  that  the 
additional  cost  incident  tJiereto  is  a  wise  investment. 


Although,  of  late  years,  the  author  has  been  specifying  the  addition  of  a 
small  percentage  of  hydrated  lime  to  the  cement  used  for  making  concrete 
in  bridgework,  with  the  dual  purpose  in  view  of  increasing  fluidity  and 
reducing  porosity,  he  has  not  called  for  blanket  water-proofing  and  flash- 
ing, excepting  where  there  was  special  reason  for  preventing  drip;  but, 
because  of  the  convincing  character  of  the  preceding  dissertation,  he  has 
decided  that  in  future,  if  his  clients  can  be  persuaded  to  stand  for  the 
additional  expense,  he  will  adopt  every  available  effective  means  in  order 
to  water-proof  his  structures  thoroughly. 

Since  the  preceding  was  written,  the  author's  attention  has  been  called 
to  an  important  paper  delivered  to  the  Brooklyn  Engineers'  Club  in  May, 


458  ECONOMICS   OF  BRIDGEWORK  Chapter  XLIII 

1916,  by  Mr.  Albert  H.  Rhett,  C.  E.,  entitled  "The  Water-Proofing  of 
Structiires  Subject  to  Stress  from  Moving  Loads  and  Temperature  Varia- 
tions." In  it  Mr.  Rhett  gives  a  short,  chronological  record  of  the  various 
unsuccessful  endeavors  to  produce  an  effective  water-proofing  for  bridge 
floors,  leading  up  to  a  successful  one  of  his  own.  In  concluding  his  inter- 
esting and  valuable  memoir  he  makes  the  following  statement : 

To  recapitulate,  then :  The  theory  evolved,  and  which  it  was  attempted  to  prove, 
is  that,  if  a  structure  subject  to  moving  load  and  temperature  variation  is  to  be  water- 
proofed, it  can  be  effected  only  through  the  medium  of  a  membrane,  incorporated  in  the 
floor,  which  fulfills  these  two  conditions: 

(1)  The  compound  element  of  this  membrane  must,  of  necessity,  be  the  eventual 

factor  upon  which  reliance  is  to  be  placed. 

(2)  The  compound,  to  fulfill  its  true  function,  must  remain  water-proof,  non- 

hardening,  elastic,  coherent,  and  adherent  at  low  temperatures  as  well 
as  high. 


CHAPTER  XLIV 

ECONOMICS    OF   MILITARY    BRIDGING 

FOREWORD 

By  Major  General  Lansing  H.  Beach,  Chief  of  Engineers,  U.  S.  Army. 

The  work  of  our  Engineers  in  France  during  the  World  War  was  some- 
thing of  which  the  whole  American  people  have  good  reason  to  be  proud. 
In  this  work  the  members  of  the  engineering  profession  showed  their 
great  versatihty  and  their  ability  to  attack  successfully  problems  previously 
unknown  to  those  without  military  training. 

There  were  many  things  to  be  learned  and  some  to  be  unlearned.  The 
Civil  Engineer,  in  general,  was  forced  to  revise  much  that  had  been  incul- 
cated in  him  during  his  earhest  studies  in  engineering,  and  confirmed  during 
the  course  of  his  professional  practice.  Possibly  the  most  important  new 
lessons  were  that,  in  a  military  construction,  time  is  of  more  importance 
than  any  other  feature  involved;  that  a  structure,  especially  a  bridge,  does 
not  have  to  be  of  uniform  strength  throughout,  but  that,  Hke  a  chain,  it 
will  answer  its  purpose  if  its  weakest  link  is  just  strong  enough  to  stand  the 
strain  which  will  be  put  upon  it ;  that  architectural  beauty  for  its  own  sake 
has  no  place  in  field  operations;  and  that  permanence  is  a  consideration  of 
such  slight  importance  that  frequently  it  does  not  enter  the  calculations 
at  all. 

The  appearaiice  and  the  lack  of  strength  occasionally  gave  the  new 
officers  of  Engineers  a  shock,  inducing  a  feeling  that  much  of  their  study  and 
practice  had  been  in  vain  and  that  much  of  their  previous  experience  could 
help  them  but  little  in  the  construction  of  emergency  bridges.  It  is,  how- 
ever, the  Engineer  best  trained  in  civil  practice  who  can  build  the  best 
emergency  structure,  if  he  will  but  properly  evaluate  the  conditions  imposed 
by  military  exigencies. 

The  Engineers  in  the  War  were  adaptable,  but  we  are  all  the  results  of 
our  education  and  training; ;  and  it  is,  therefore,  not  amiss  to  bring  to  the 
attention  of  the  members  of  the  profession  at  large  certain  principles 
which  they  may  learn  in  time  of  peace  and  be  prepared  to  apply  in  time  of 
war,  and  thus  avoid  having  to  acquire  this  knowledge  in  the  face  of  the 
enemy,  when  the  lives  of  thousands  of  their  fellow  citizen-soldiers  are  at 
stake.  Victory  and  defeat,  the  rise  and  the  fall  of  nations,  have  often 
depended  upon  seeming  trifles.  It  is  conceivable  that  an  engineering 
failure  in  war  may  involve  the  extinction  of  a  state. 

459 


460  ECONOMICS   OF  BRIDGEWORK  Chapter  XLIV 

The  eminent  author  of  this  book  has  made  a  profound  study  of  the 
economics  that  apply  to  many  of  the  problems  which  the  Civil  Engineer  is 
called  upon  to  solve,  and  it  will  be  widely  read  by  all  engineers  who  are 
determined  to  be  in  the  forefront  of  their  profession.  It,  therefore,  seems 
most  fitting  that  in  this  book  there  should  appear  a  chapter  deahng  with  the 
principles  which  must  apply  to  a  phase  of  the  work  of  the  Military  Engineer, 
work  which  any  one  of  the  many  readers  may  be  called  upon  at  some  time 
to  carry  on. 

Colonel  P.  S.  Bond,  Corps  of  Engineers,  U.  S.  Army,  was  selected  to 
prepare  this  chapter  because  of  his  intimate  knowledge  of  the  subject, 
acquired  by  study  and  by  practice.  He  has  presented  it  clearly  and 
logically,  pointing  out  the  essential  differences  which  must  prevail  between 
the  principles  that  govern  the  building  of  bridges,  according  as  they  are 
intended  for  military  use  or  to  serve  peaceful  purposes. 

He  has  stressed  particularly  the  all  important  time  element  in  war 
enterprises,  and  has  shown  that  what  in  civil  practice  might  be  wilful  waste, 
in  war  may  be  the  greatest  of  all  economic  measures.  In  fact,  so  tre- 
mendous is  the  cost  of  conducting  a  modern  war,  it  is  hardly  too  much  to 
say  that  any  expenditure  of  money  or  of  material  which  will  shorten  its 
duration  is  easily  justified.  A  careful  reading  of  this  chapter  is,  therefore, 
earnestly  recommended  to  all  of  those  to  whom  the  Army  must  look  for 
help  when  next  we  are  called  upon  to  take  up  arms  in  the  defense  of  our 
rights  and  the  rights  of  humanity.  , 


Economics  of  Military  Bridging 

Streams  constitute  one  of  the  greatest  obstacles  to  military  operations, 
and  bridge  building  is,  accordingly,  one  of  the  chief  duties  of  the  military 
engineer. 

Fundamental  Economics  of  Military  Engineering 

Military  bridge  engineering  is  an  adaptation,  in  a  simple  and  frequently 
crude  and  makeshift  form,  of  civil  practice  to  military  needs.  The  finida- 
mental  difference  between  civil  and  military  practice  is  in  their  economic 
aspects.  The  technical  details  of  military  bridges  are  characterized  by 
extreme  simplicity,  which  is  demanded  by  the  conditions  under  which  they 
must  be  Ijuilt.  They  will  present  little  difficulty  to  the  engineer  having  a 
good  general  knowledge  of  civil  practice. 

But  the  successful  practice  of  military  engineering,  including  bridging, 
doinands  a  knowledge  of  the  economic  principles  which  are  specially  appli- 
cable to  warfare.  Mistakes  in  economic  judgment  will  have  more  far- 
reaching  and  disastrous  consequences  in  war  tiian  in  peace — there  will  be 
greater  opporl  unities  for  tremendous  i)rofits  or  ruinous  losses.     A  practical 


ECONOMICS  OP  MILITARY  BRIDGES  461 

knowledge  of  economic  principles  is,  accordingly,  of  greater  importance 
than  a  knowledge  of  technical  details.  It  will,  therefore,  be  of  interest  to 
consider  these  principles  m  their  application  to  warfare. 

In  war  the  highest  economy  is  victory,  and  the  greatest  waste  is  defeat; 
consequently,  anything  which  contributes  to  victory  and  evades  defeat  is 
justifiable,  however  great  its  cost  or  the  incidental  waste  involved — of 
course  within  the  hmits  of  reason  and  common  sense.  A  free  and  rapid 
expenditure  of  available  resources  m  war  is  not  waste,  but  the  highest 
form  of  economy  when  it  contributes  to  early  victory.  The  march  of 
events  is  rapid  in  modern  war.  A  few  days,  even  a  few  hours,  have  decided 
the  issue  of  battle.  The  Commander  does  not  ask  his  Engineer,  "How 
much  will  your  bridge  cost?  "  but,  "  How  soon  will  it  be  ready?  " 

In  civil  bridge  construction  the  essential  requirements,  in  their  usual 
order  of  importance,  are.  initial  cost,  safety,  durability  or  permanence, 
time  required  for  construction,  and  aesthetics.  The  time  required  for 
construction  is  of  importance  chiefly  in  so  far  as  it  affects  the  financial 
returns  on  the  investment.  A  considerable  time  spent  in  design  and  other 
preliminaries  to  construction,  and  on  the  work  itself,  will  usually  be  amply 
justified  by  a  material  saving  in  cost. 

The  Time  Factor  Substituted  for  the  Cost  Factor 

In  military  construction  some  of  these  desiderata  entirely  disappear, 
and  the  order  of  importance  of  others  is  reversed.  In  particular,  the  time 
of  construction  becomes  of  paramount  importance — the  time  factor  is 
substituted  for  the  cost  factor  as  the  principal  consideration.  In  sharp 
contrast  to  civil  practice,  we  find  that  any  cost  will  be  justified,  if  it  results 
in  saving  of  valuable  time  at  a  critical  juncture.  As  a  consequence  of  this, 
the  construction  of  military  bridges  is  conducted  with  feverish  rapidity. 
The  highest  achievement  of  the  military  bridge  builder  is  a  structure  just 
sufficient  for  its  immediate  purpose,  erected  in  the  minimum  time,  without 
undue  regard  for  cost,  appearance,  or  durability.  Time  is  always  the  chief 
— often  the  only — consideration;  delay  is  always  inadmissible;  and  suc- 
cess is  the  only  criterion  by  which  the  engineer  will  be  judged. 

In  civil  construction  time  is  of  importance;  but  it  is  seldom  necessary 
to  sacrifice  cost,  safety,  and  all  other  considerations  to  gain  time.  A  delay 
for  a  moderate  period  will  usually  not  be  hurtful.  In  military  operations, 
on  the  contrary,  a  delay  of  a  few  days,  or  even  a  few  hours,  may  mean 
failure  instead  of  success.  A  similar  situation  sometimes  arises  in  civil 
bridge  practice,  as,  for  example,  when  it  is  necessary  to  restore  traffic  on  an 
important  main-line  railroad  after  a  bridge  has  been  destroyed  by  fire  or 
flood.  In  such  a  situation  the  economics  are  similar  to  those  of  warfare; 
and  military  methods  of  procedure  would  there  be  appropriate. 

The  Principle  of  "Bare  Necessities  Only  " 

Military  bridges  are  always  required  in  the  least  possible  time,  and 
there  will  very  often,  perhaps  usually,  be  a  dearth  of  building  material. 


462  ECONOMICS   OF  BRIDGEWORK  Chapter  XLIV 

It  is,  accordingly,  a  fundamental  economic  principle  of  military  construc- 
tion that  bare  necessities  alone  should  be  provided  for.  An  engineer  who 
wastes  valuable  time  and  material  constructing  a  bridge  wide  enough  and 
strong  enough  to  carry  heavy  motor  trucks,  when  the  need  of  the  instant 
is  a  simple  foot-bridge  over  which  a  body  of  infantry  may  pass  at  once  to  a 
critical  point  of  the  field,  has  manifestly  failed  to  grasp  this  fundamental 
economic  principle. 

Safety  and  Permanence 

The  civil  engineer  "builds  for  posterity."  Whatever  the  type  of 
bridge  adopted,  it  is  usually  constructed  in  as  enduring  a  faslnon  as  the 
funds  available  and  the  material  employed  will  permit.  The  useful  life 
of  the  bridge  is  ordinarily  a  measure  of  the  skill  of  its  builder. 

The  military  engineer  builds  to  meet  the  exigency  of  the  moment. 
He  is  lacking  in  skill  if  he  expends  time  in  order  that  his  bridge  may  endure 
unduly  long  beyond  the  period  it  is  needed,  which  in  no  case  exceeds  the 
duration  of  the  war,  and  is  often  limited  to  that  of  a  single  action.  The 
thoroughness  of  his  work  should  be  sufficient  unto  the  immediate  needs — 
and  no  more  than  sufficient.  Nicety,  finish,  refinement,  and  permanency, 
for  their  own  sake,  are  to  be  avoided.  The  military  bridge  should  have  no 
beauty  except  that  which  is  inherent  in  utilitarianism. 

In  civil  construction  great  weight  is  properly  given  to  the  factor  of 
safety  and  to  the  durability  or  permanence  of  the  structure.  In  military 
procedure  these  considerations  have  far  less  weight.  The  factor  of  safety 
need  seldom  be  as  great,  although  this  will  depend  to  some  extent  on  the 
situation.  Where  a  military  force  is  entirely  dependent  on  a  single  line 
of  supply,  the  bridges  on  this  line  should  have  a  factor  of  safety  as  great 
or  nearly  as  great,  as  would  be  employed  in  civil  practice.  But  ordinarily, 
in  the  combat  zone  at  least,  the  saving  in  time  and  material  which  results 
from  using  a  factor  of  safety  of  2  instead  of  4  or  5  will  more  than  compen- 
sate the  risk  involved  in  the  possible  collapse  of  structures.  The  risks 
attendant  upon  military  operations  are  so  numerous  and  so  great  that  the 
slight  additional  risk  of  a  small  factor  of  safety  is  of  minor  significance. 

Permanence  is  of  negligible  importance  in  military  construction,  inas- 
much as  the  structures  will  never  be  required  beyond  the  duration  of 
the  war,  and  frequently  for  much  shorter  periods.  It  is  generally  good 
economy  first  to  meet  the  exigency  of  the  moment,  and  later  to  repair, 
strengthen,  or  even  replace  the  structure,  should  this  be  necessary  by  reason 
of  continued  need.  The  time  for  which  any  military  structure  will  be 
required  is  usually  short,  and  always  uncertain,  so  that  it  is  not  good 
economy  to  look  too  far  into  the  future. 

Warfare  is  an  economic  art,  no  less  than  any  of  the  pursuits  of  peace.' 
In  war  we  have  a  mission  to  perform,  which  is  the  achievement  of  victory; 
and  this  mission  sliould  ])e  acconiplislied  with  the  least  ])ossible  expenditure 
of  blood  and  treasure — in  oilier  words,  in  the  most  economical  fashion. 


ECONOMICS   OF   MILITARY   BRIDGES  463 

This  demands  that  victory  be  won  in  the  shortest  possible  time,  since  the 
cost  of  war  is  nearly  proportional  to  the  duration  of  the  conflict.  More- 
over, in  the  prosecution  of  the  conflict  itself,  victory  comes  to  the  com- 
batant who  can  most  rapidly  mass  his  resources  of  men  and  materials  at 
the  critical  points.  It  is  for  these  reasons  that  time  is  so  important  an 
element  in  all  military  operations,  including  construction. 

Waste  not  Justifiable 

The  achievement  of  our  purpose  in  war  calls  for  a  rapid  expenditure  of 
both  life  and  material.  It  is  the  duty  of  the  Commander,  however,  to 
expend  in  the  most  economical  manner  possible  the  resources  which  the 
nation  by  painful  sacrifice  has  placed  at  his  disposal;  and  the  same  obhga- 
tion  rests  upon  all  his  subordinates.  But  great  expenditures  to  accom- 
plish great  results  are  not  wasteful. 

The  engineer  must  thoroughly  disabuse  his  mind  of  any  belief  that 
military  necessity  ever  calls  for  or  justifies  waste  of  the  nation's  resources; 
but  he  must  not  allow  a  penny-wise  inclination  toward  economy  of  material 
or  money  to  cause  him  to  overlook  the  greater  necessity  for  economy  of 
time.  Material  should  be  freely  expended  to  save  time,  but  it  should 
never  be  wasted.  However  great  the  resources  of  the  nation,  there  is 
always  a  dearth  of  construction  material  in  war,  due  not  alone  to  lack  of 
material  but  also  to  lack  of  transportation  facilities  for  dehvering  it  at  the 
places  where  it  is  required.  A  reckless  use  of  material  in  one  locality  may 
mean  the  failure  of  important  operations  in  some  other  place  where  the 
material  thus  wasted  is  needed.  A  small  saving  of  material  must  not  be 
made  at  the  expense  of  a  great  waste  of  time;  but  the  soldier  who  deliber- 
ately or  carelessly  wastes  any  useful  material  is  guilty  of  highly  unpatriotic, 
not  to  say  criminal,  conduct. 

Classes  of  Military  Bridges 

There  are  two  general  classes  of  military  bridges; 

(o)  Those  constructed  in  rear  of  the  battle  lines,  in  the  zone  of  com- 
munications, not  in  the  immediate  presence  of  the  enemy. 

(6)  Those  constructed  at  the  front,  within  the  combat  zone  or  the  area 
subject  to  hostile  fire  and  raids. 

Structures  of  the  first  class  are  erected  for  purposes  and  under  conditions 
approximating  those  of  civil  construction  in  time  of  peace.  The  need  for 
such  bridges  is  determined  mainly  from  strategical  considerations,  and  they 
seldom  have  any  intimate  relation  to  the  tactical  operations  of  the  com- 
batant forces.  As  compared  to  bridges  within  the  zone  of  tactical  activi- 
ties, they  are  usually  needed  for  a  relatively  long  period — from  several 
months  to  the  duration  of  the  war.  They  are  required  to  carry  heavy  loads. 
They  may  be  constructed  by  non-combatant  troops,  by  hired  civilian  labor, 
or  even  by  contract.  Construction  plant,  similar  to  that  employed  in 
civil  works,  will  be  utilized  whenever  it  is  available.     With  the  exception 


464  ECONOMICS   OF   BRIDGEWOEK:  Chapter  XLIV 

of  the  facts  that  they  are  less  permanent  in  their  nature,  and  that  no  con- 
sideration is  given  to  the  appearance  of  the  finished  structures,  these 
bridges  are  built  in  accordance  with  the  recognized  rules  of  good  civil 
practice. 

Structures  of  the  second  class,  those  at  the  front,  are  erected  to  meet  the 
immediate  tactical  requirements  of  the  combatant  forces.  They  are  usu- 
ally in  the  form  of  hasty  makeshifts  of  a  crude  character,  and  are  built  by 
combatant  troops  in  accordance  with  the  economic  principles  of  warfare 
heretofore  enunciated. 

There  are  no  sharp  lines  of  demarcation  between  civil  practice  and  mili- 
tary bridges  of  the  first  class,  nor  between  military  bridges  on  the  lines  of 
communication  and  those  at  the  battle  front.  Mihtary  economics  are 
occasionally  applicable  to  civil  practice,  and  vice  versa. 

Types  of  Military  Bridges 

The  particular  type  of  bridge  to  be  employed  in  any  situation  depends  on 
the  nature  of  the  stream — its  width,  depth,  swiftness  of  current,  and 
liability  to  flood;  the  character  of  the  approaches;  the  labor,  plant,  and 
materials  available;  and  the  loads  to  be  carried.  Every  type  of  bridge 
known  to  civil  practice  has  been  employed  for  military  purposes,  including 
pile  and  framed  trestles,  and  cantilever,  truss,  girder,  suspension,  floating, 
and  arch  bridges.  The  last  mentioned,  either  of  steel  or  masonry,  are 
very  rarely  used,  and  only  on  the  fines  of  communication.  Military  bridges 
are,  in  general,  crude,  impermanent,  and  makeshift  forms  of  their  civil 
prototypes. 

Any  bridge  for  which  the  erection  requires  a  long  time  and  an  elaborate 
and  heavy  plant  will  usually  be  avoided  in  military  practice,  and  is  out  of 
the  question  for  any  tactical  purpose.  The  considerations  calHng  for  such 
bridges  in  civil  practice  will  usually  have  much  less  weight  in  time  of  war. 
For  example,  a  long-span-truss  or  cantilever  bridge  may  be  adopted  in 
order  to  avoid  the  expense  of  very  deep  foundations,  to  evade  danger  from 
floods,  or  to  meet  the  requireinents  of  navigation.  Deep  foundations  are 
out  of  the  question  in  emergency  military  bridging,  and  are  evaded  by  the 
use  of  the  floating  equipage,  by  portable  (sectional)  trusses,  by  long-span 
suspension-bridges  for  very  light  loads,  or  by  ferries  for  occasional  traffic 
too  heavy  for  the  bridges.  Danger  from  flood  is  avoided  in  a  similar  man- 
ner; but,  as  the  period  for  which  a  military  bridge  will  be  required  is 
always  relatively  short,  it  will  frequently  be  bettor  to  run  the  rechicod  risk 
of  flood  damage,  rather  than  spend  nuich  time  in  guarding  against  it.  If 
the  flo(Kl  risk  be  really  great  and  imminent,  it  is  best  avoided  by  using  the 
floating  equipage,  \mless  a  clear  span  of  moderate  length  will  meet  the 
situation.  In  war  the  rights  of  (uvil  navigation  must  give  way  to  military 
necessity.  Military  traffic,  both  over  the  ])ri(lge  and  along  the  stream, 
may  be  regulated  so  as  to  intcn'fere  with  each  oi  hei-  as  fit! h^  as  possible,  draw 
spans  being  provided,  if  necessary,  for  the  i)assage  of  vessels. 


ECONOMICS  OF  MILITARY  BRIDGES  465 

The  Typical  Military  Bridge 

The  typical  military  bridge,  therefore,  since  it  must  be  erected  in  a 
short  time  and  without  elaborate  plant,  will  be  characterized,  as  a  rule,  by 
shallow  foundations,  by  a  relatively  large  number  of  piers  or  supports  with 
correspondingly  short  spans,  and  by  structural  members  of  small  size,  light 
weight,  and  great  simplicity.  If  we  add  that  timber  is  the  material  most 
frequently  employed,  this  dehneation  of  the  typical  military  structure  wiU 
be  recognized  as  a  description  of  the  short  span,  framed-trestle-and-stringer, 
timber  bridge;  and,  in  fact,  this  is  the  type  employed  in  the  majority  of 
cases  in  military  practice.  If  we  now  permit  the  occasional  use  of  pile 
trestles  instead  of  framed  trestles,  I-beams  in  place  of  wooden  stringers, 
and  simple  wooden  or  sectional  steel  trusses  for  greater  spans,  and  include 
the  standard  floating  equipage,  we  shall  have  enabled  the  military  bridge 
builder  to  meet  nearly  all  situations  with  which  he  will  be  confronted. 

Some  of  the  economic  features  of  the  more  usual  types  of  military 
bridges  will  now  be  considered. 

Framed  Trestles 

The  framed  trestle  requires  no  plant,  other  than  simple  tackle,  for  its 
erection.  It  is  readily  constructed  from  a  great  variety  of  materials,  and 
by  unskilled  labor;  and  it  meets  the  majority  of  emergency  situations. 
The  framed  trestle,  as  we  have  seen,  is  accordingly  the  favorite  type  of 
support  in  hasty  military  bridging  in  the  combat  zone.  The  usual  form  of 
bent  is  the  simple,  one-plane  type  with  cap,  sill,  two  or  more  posts  or  legs, 
and  diagonal  sway-bracing. 

The  trestle  will  be  stiff er  against  lateral  stresses,  if  the  outer  posts  be 
inclined  or  battered;  but  with  unskilled  labor  it  is  easier  to  make  all  the 
posts  vertical.  If  pieces  of  sufficient  length  are  available,  the  stiffness 
may  be  greatly  increased  by  extending  both  the  cap  and  the  sill  a  foot  or 
more  beyond  the  outer  posts  and  attaching  the  sway  braces  to  the  ends  of 
the  cap  and  sill  as  well  as  to  each  post. 

If  the  depth  of  water  is  such  that  the  trestles  tend  to  float  up,  the  bot- 
toms of  the  posts  may  be  boxed  in  and  the  compartments  filled  with  stone. 

If  the  river  bottom  be  of  low  bearing  power,  a  sill  of  greater  width  than 
that  of  the  posts  may  be  employed.  The  bearing  power  of  the  bottom 
may  be  increased  by  brush  mattresses  or  fascines,  wooden  mud-sills  (where 
the  water  is  shallow),  or  rip-rap.  It  is  usually  well  worth  while  to  resort 
to  such  measures,  in  order  to  avoid  the  use  of  piles. 

Economic  Span  of  Trestles 

The  proper  economic  span  of  pile  or  framed  trestles  is  determined  by 
balancing  the  time  and  material  required  for  the  bents  against  that  required 
for  the  stringers.  The  problem  cannot  be  solved  with  mathematical  pre- 
cision.    It  depends  upon  the  height  of  the  trestles,  the  difficulty  of  placing 


466  ECONOMICS   OF  BRIDGEWORK  Chapter  XLIV 

the  bents,  the  load  to  be  carried,  the  materials  available  which  are  suitable 
for  bents  or  stringers,  respectively,  etc.  Crooked  stringers  are  an  unmiti- 
gated nuisance;  and  in  a  hasty  bridge,  when  only  a  scrubby  growth  of 
timber  is  available,  it  may  be  impossible  to  secure  reasonably  straight 
pieces,  except  in  very  short  lengths.  In  such  a  case  the  spans  must  be 
short.  On  the  other  hand,  if  bents  must  be  built  of  round  timber,  and  if 
good  dimensioned  material  is  available  for  stringers,  the  number  of  trestle 
bents  may  be  reduced  and  the  span-length  increased.  If  the  loads  to  be 
carried  are  moderate,  longer  spans  will,  of  course,  be  permissible.  The 
engineer  must  scan  the  situation  and  come  to  a  decision  based  on  his  experi- 
ence and  common  sense. 

However,  it  is  possible  to  state  the  usual  limits  of  good  practice.  Under 
average  conditions  the  proper  economic  span  of  hasty,  mihtaiy  trestle- 
bridges  is  from  10  to  15  ft.,  averaging  about  12  ft.  For  heavy  standard 
bridges,  designed  to  carry  the  greatest  loads  of  the  army,  the  maximum 
practicable  span,  when  wooden  stringers  are  employed,  is  16  ft.,  which 
length  requires  16-inch  stringers.  If  I-beams  be  employed,  this  span  may 
be  increased  to  22  ft.  For  any  length  over  this,  either  strutted  beams  or 
some  form  of  truss  should  be  adopted.  When  very  tall  trestles  are  required, 
it  will  often  be  good  economy  to  increase  the  span  by  using  simple  trusses, 
or  by  strutting. 

In  practice,  the  number  of  bents  and  the  span  of  trestles  are  frequently 
determined  by  the  material  actually  available  for  stringers.  These  must  be 
able  to  carry  the  required  loads;  and,  whenever  possible,  they  are  furnished 
in  standard  sizes  and  lengths  for  this  purpose.  Where  the  material  for 
stringers  has  been  cut  to  a  given  length,  the  span  of  the  trestles  is,  of  course, 
thereby  fixed. 

For  moderate  loads,  tall  trestles  may  be  built  in  single  stories,  if  material 
of  suitable  length  is  available.  For  the  standard  heavy  trestles  the  follow- 
ing rules  have  been  adopted: 

Up  to  16  ft.,  one-story  bents  with  one-story  bracing. 

From  16  to  24  ft.,  one-story  bents  with  two-story  bracing. 

Over  24  ft.,  two  or  more  stories. 

The  need  for  longitudinal  bracing  between  bents  depends  on  the  height, 
the  span,  and  the  nature  of  the  traffic.  If  the  height  of  the  trestle  exceeds 
7  ft.  and  the  span  is  greater  than  10  ft.,  longitudinal  bracing  should  be 
placed  in  each  alternate  bay.  For  considerable  heights  it  is  well  to  brace 
all  bays,  if  practicable.  In  multiple-story  bents  each  story  should  be 
separately  braced. 

Spar-Bridges 

The  term  spar-bridge  is  a  general  designation  for  a  military  structure  of 
rough  (round)  timber.  Such  bridges  ai-e  built  from  necessity  when  better 
material  is  not  available.  They  will  continue,  as  in  the  past,  to  be  a 
characteristic  type  in  the  operations  of  relatively  small  and  poorly  equipped 


ECONOMICS   OF   MILITARY   BRIDGES  467 

forces,  especially  in  sparsely  settled  countries  under  bad  conditions  as  to 
transportation. 

Because  of  lack  of  other  fastening  materials,  spar-bridges  are  often 
assembled  by  lashing  the  trestles.  In  such  cases  it  is  impossible  to  use 
"rider"  sills  and  caps,  placed  on  the  tops  and  bottoms  of  the  posts;  hence 
"ledgers,"  attached  a  short  distance  below  the  tops  and  above  the  bottoms 
of  the  posts,  are  employed.  Stringers  are  also  lashed,  and  decking  is 
secured  by  means  of  side-rails  placed  over  and  lashed  down  to  the  outer 
stringers.  The  term  "spar-bridge"  is  generally  used  to  describe  such  a 
characteristically  military  structure.  Whenever  possible,  however,  even 
bridges  of  round  timber  should  be  roughly  framed,  have  rider  caps  and  sills, 
and  be  fastened  with  bolts,  spikes,  or  dogs. 

A  special  form  of  spar-bridge,  known  as  the  lock-spar,  is  a  structure  in 
which  the  trestle  bents  are  tilted  towards  each  other  and  locked  together 
or  to  a  frame  placed  between  two  bents  (double  lock).  These  are  of  very 
limited  application,  but  may  occasionally  be  used  to  advantage  in  spanning 
a  deep  gorge.  With  the  double  lock  the  bridge  is  practicable  in  spans  up 
to  50  ft.  for  moderate  loads. 

Spar-bridges,  especially  when  lashed,  if  of  necessity  employed  in  the 
first  instance  for  a  hasty  crossing,  should  be  replaced  promptly  by  a  better 
type  of  bridge,  as  they  are  unsuitable  for  continued  heavy  traffic. 

Pile  Trestles 

Framed  bents,  as  they  are  so  easily  erected  without  plant,  will  be  gen- 
erally employed  when  the  bottom  is  firm  enough  to  support  them,  and 
when  scour  can  be  prevented.  When  the  bottom  is  of  very  low  bearing- 
power,  or  subject  to  scour,  as  in  the  case  of  soft  mud  or  shifting  sand,  piles 
will  be  required.  Pile  bents  have  the  disadvantage  of  necessitating  longer 
pieces,  more  time,  and  the  use  of  a  pile  driver  for  their  erection.  How- 
ever, they  are  required  in  many  situations,  especially  for  railroad  bridges, 
where  even  a  slight  settlement,  such  as  might  result  from  the  use  of  framed 
bents,  would  be  dangerous.  Accordingly,  a  number  of  efficient  portable 
pile-drivers  should  form  part  of  the  equipment  of  an  army;  and,  when 
such  are  available,  pile  trestles  will  often  be  preferred  to  framed  ones. 
Pile-trestle  bents  are  subject  to  the  same  economic  considerations  as 
framed-trestle  bents,  except  that,  being  stiffer,  they  require  less  bracing. 

Trusses 

For  military  purposes  the  truss  has  all  the  economic  advantages  it  pos- 
sesses in  civil  use.  It  is  employed  to  reduce  the  number  of  trestle  bents, 
or  other  type  of  piers,  when  the  construction  of  the  said  piers  is,  for  any 
reason,  particularly  difficult.  Trusses  are  also  used  to  give  greater  clear- 
ance as  a  measure  of  flood  protection,  or  to  span  deep  chasms  or  streams 
without  intermediate  supports. 

Military  trusses  must  usually  be  erected  without  falsework,  and  with 


468  ECONOMICS   OF  BRIDGEWORK  Chapter  XLIV 

the  aid  of  only  animals,  simple  tackle,  and  gin-poles  or  A-frames.  There 
will  be  difficulty  in  transporting  long  pieces  for  such  trusses.  Where  they 
must  be  constructed  in  the  combat  zone,  the  span,  consequently,  is  limited 
to  40  or  50  ft.  in  the  usual  case.  Larger  trusses  may  occasionally  be  built 
in  place;  and  when  plant  is  available,  as  in  the  rear  areas,  much  greater 
spans  will  be  practicable. 

Improvised  trusses  must  be  constructed  of  wood,  preferably  sawed 
material,  and  steel  tie-rods  or,  in  exceptional  cases,  cables.  Accordingly, 
simple  triangular  (King  post),  Howe,  and  Pratt  trusses  (generallj-  erect  or 
through)  will  be  the  usual  types.  Where  only  hght  material  is  available, 
lattice  or  bow-string  trusses  may  be  employed.  These  types  should  be 
built  as  nearly  as  possible  in  accordance  with  civil  practice  in  similar 
structures.  Joints  should  be  as  simple  as  practicable,  requiring  a  mini- 
mum of  expert  carpentering.  Round  timbers  may  be  used  in  the  simpler 
forms  of  trusses,  if  dimensioned  stuff  is  not  available.  Deck  spans  may 
be  employed  for  reasons  similar  to  those  which  would  dictate  their  adop- 
tion in  civil  practice. 

Sectional  Trusses  and  Girders 

Sectional,  portable,  or  "knock-down"  trusses  and  girders,  in  wood  and 
especially  in  steel,  were  the  principal  development  in  military  bridging 
during  the  World  War.  They  were  demanded  by  the  augmented  density 
of  traffic,  and  especially  by  the  tremendous  increase  in  mihtaiy  loads, 
which  now  include  heavy  motor-trucks,  artillery  of  great  caHbers,  tractors, 
and  30-ton  tanks.  The  improvised  bridges,  long  characteristic  of  mihtary 
operations  on  a  smaller  scale,  were,  alone,  inadequate  to  meet  the  unprec- 
edented situation.  It  was  recognized  that  there  was  needed  some  form 
of  standardized  superstructure,  easily  transported,  rapidly  erected,  adapt- 
able to  varying  spans,  and  capable  of  carrying  the  heaviest  loads.  This 
demand  was  best  met  by  portable,  sectional,  steel  girders  and  trusses; 
and  various  types  of  such  structures  were  developed  by  the  British,  French, 
and  American  Armies. 

As  usual  in  such  cases,  a  great  variety  of  types  was  evolved;  but,  in 
the  interests  of  efficiency,  the  number  of  such  should  be  limited,  and  each 
should  be  made  adaptable  to  varying  conditions. 

For  the  American  Army,  sectional  steel  girders  (I-beams)  for  spans 
up  to  30  ft.,  and  sectional  steel  trusses,  for  spans  from  33  to  90  ft.,  were 
designed.  The  British  employed  sectional  trusses  in  spans  up  to 
180  ft. 

In  order  to  permit  transportation  in  motor  trucks,  the  truss  sections 
(panels  or  bays)  were  limited  to  11  ft.  3  ins.  Spans  from  33  to  90  ft.,  in 
increments,  could  be  erected  with  this  equipage.  The  sections  were  con- 
nected for  erection  by  bolts,  no  field  rivets  being  used.  These  trusses  can 
be  (unployed  with  any  ty])(^  of  sujiport  or  \V\cr.  The  truss  is  erected  with- 
out falsework,  being  bolted  together  on  one  bank,  and  placed  by  launch- 


ECONOMICS    OF   MILITARY   BRIDGES  469 

ing  with  the  aid  of  tackle  and  an  A-frame  derrick,  or  by  a  counter-poise  of 
additional  sections  of  truss. 

It  is  certain  that  sectional  steel  girders  and  trusses  will  be  used  on  a  vast 
scale  in  future  wars  of  any  grea.t  magnitude. 

Portable  girder-spans,  usually  of  timber,  complete  with  flooring,  in  one 
or  two  sections,  are  provided  for  the  passage  of  foot  troops  and  artillery- 
over  trenches,  ditches,  and  small  shell-holes,  in  following  up  an  attack. 
These  bridges  are  transported  on  combat  wagons  or  artillery  caissons. 

Cribs 

Cribs  may  be  usefully  employed  for  piers  on  very  unstable  bottoms, 
especially  when  there  is  a  swift  current,  and  for  abutments.  They  have 
the  advantages  that  they  require  no  plant,  and  can  be  built  of  short  pieces 
of  almost  any  material.  Cribs  have  greater  power  of  resistance  to  floods, 
ice,  and  drift  than  have  simple  trestles,  provided  they  are  solidly  con- 
structed and  filled  with  stone.  Cribs  are  often  employed  as  foundations 
for  framed  trestles,  the  crib-work  being  carried  above  ordinary  flood 
level. 

Trenches,  ditches,  shell-holes,  and  small  ravines  can  be  made  passable 
by  filUng  them  with  any  debris  that  may  be  at  hand. 

An  interesting  development  of  the  World  War  was  a  small  cube  oi 
crib  of  structural  steel,  any  number  of  which  could  be  bolted  together  to 
form  a  bridge  abutment. 

Suspension  Bridges 

Suspension  bridges  are  occasionally  employed  in  military  operations. 
For  spans  exceeding  50  ft.,  when  no. plant  and  no  sectional  trusses  are  avail- 
able, they  will  sometimes  meet  the  situation.  For  military  purposes  they 
have  the  advantage  that  the  only  essential  parts  are  the  cables,  which  are 
easily  transported.  If  these  are  at  hand,  the  remaining  portions,  being 
small  and  light,  can  usually  be  obtained  in  any  locality.  Light  suspen- 
sion bridges  are  easily  erected  without  plant.  When  materials  for  a  fixed 
bridge  must  be  carried  with  a  rapidly-moving  column,  the  suspension  type 
has  the  advantage  of  requiring  the  least  material,  for  a  given  span  and 
capacity,  of  any  kind  of  bridge.  Moreover,  its  parts,  being  small,  are 
easily  transported  and  handled. 

The  suspension  bridge  is  specially  applicable  to  long  spans  combined 
with  light  loads,  but  even  in  such  situations  the  ponton  equipage  or  ferries 
will  usually  be  preferred  for  stream  crossings.  Hasty  suspension  bridges 
may  be  built  to  carry  wagons,  but  for  motor  traffic  they  are  unsuitable. 
In  general,  they  are  used  only  for  foot  bridges  of  relatively  long  span. 
Their  ideal  function  is  for  foot  traffic  and  pack  transportation  over  wide 
and  deep  ravines  in  mountainous  country,  where  the  ponton  equipage  or 
sectional  trusses  are  not  applicable. 

Because  of  the  difficulty  of  handling  in  the  field,  cables  are  generally 


470  ECONOMICS   or   BRIDGEWORK  Chapter  XLIV 

limited  to  one  inch  diameter,  as  many  as  necessary  being  employed. 
Standing  trees  are  utilized  as  towers  and  anchorages  when  this  is  feasible. 

It  will  usually  be  impracticable  to  insure  vertical  reactions  on  the 
towers;  and  as  roller  bearings  are  not  employed,  the  said  towers  should  be 
of  the  sawhorse-trestle  type  and  well  braced,  in  order  effectively  to  resist 
the  overturning  moment.  The  sag  of  cables  usuallj'  employed  for  mihtarj'' 
bridges  is  from  ^^  to  y  of  the  span.  Oscillation  and  undulation  are  limited 
by  the  usual  methods,  such  as  lateral  bracing  of  the  roadway,  trussing  the 
handrails,  drawing  the  cables  together  at  the  center,  gujdng,  etc.  While 
materials  for  light  suspension  bridges,  excepting  only  the  cables,  may 
usually  be  obtained  locally,  erection  will  be  greatly  facilitated  if  adjustable 
suspension  rods  (slings  or  hangers)  are  provided  in  advance. 

Ponton  or  Floating  Bridges 

The  construction  of  any  type  of  fixed  bridge  is  at  best  a  slow  process. 
Indeed,  in  the  case  where  an  army  with  heavy  artillery  and  trains  is  con- 
fronted by  a  wide  and  deep  crossing,  the  construction  of  a  fixed  bridge 
might  require  weeks,  even  months,  of  time — in  fact  it  might  prove  utterly 
impossible  under  some  field  conditions,  for  instance,  in  the  absence  of  heavy 
and  elaborate  construction  plant.  Tactical  requirements  cannot  brook  such 
delays;  and,  to  meet  situations  of  this  kind,  some  form  of  portable  bridge, 
with  floating  supports  and  capable  of  extremely  rapid  installation,  is  abso- 
lutely indispensable.  Accordingly,  all  modern  armies  are  equipped  with 
such  bridges,  which  are  known  as  ponton  or  floating  equipage. 

The  floating  equipage  which  up  to  the  present  has  been  used  in  our  own 
army  (except  the  foot-bridge)  was  devised  prior  to  the  Civil  War,  and  has 
been  employed  with  conspicuous  success  since  that  time.  It  is  a  tribute  to 
the  wisdom  of  those  who  designed  it  that,  in  over  60  years,  no  radical 
changes  in  the  equipage  have  had  to  be  made.  This  standard  equipage 
is  of  the  utmost  simplicity,  consisting  merely  of  any  number  of  boats, 
called  pontons,  which  are  anchored  in  position  and  connected  by  stringers 
or  "balk,"  resting  on  the  gimwales  of  the  boats,  on  which  stringers  the  deck 
planks  or  "chess"  are  laid,  the  whole  being  secured  by  lashings.  For 
shallow  portions  of  the  stream,  near  the  banks,  portable,  collapsible 
trestles  take  the  place  of  the  boats. 

There  are  three  forms  of  ponton  equipage,  a  heavy  wagon  bridge,  a 
light  wagon  bridge,  and  a  foot-bridge,  the  latter  devised  during  the  World 
War.  The  heavy  pontons  are  of  wood,  having  an  available  su]^poi-ting 
power  of  9|  tons  each.  The  hght  pontons  are  collapsible  wooden  frames, 
covered  with  water-proof  canvas,  and  have  a  supporting  power  of  6  tons 
each.  The  portable  foot-l)ridge  employs  miniature  canvas  pontons  and 
provides  a  path  2  ft.  wide. 

Th(!  advantages  of  this  type  of  bridge  are  its  portability  and  the  extreme 
rapidity  with  which  it  can  ])e  installed.  The  ajiproximate  wcMghts  of  the 
material  per  running  foot  of  bridge  are  as  follows:  heavy  equij^age,  170  lbs; 


ECONOMICS   OF   MILITARY   BRIDGES  471 

light  equipage,  130  lbs.;  foot-bridge,  16  lbs.  One  "division"  (225  ft.  of 
bridge)  of  the  heavy  equipage  requires  16  wagons  to  transport  it,  and 
covers  a  road  space  of  about  300  yards.  One  division  (186  ft.  of  bridge) 
of  the  light  equipage  requires  14  wagons  and  a  road  space  of  about  250  yds. 
One  division  (285  ft.  of  bridge)  of  the  foot-bridge  can  be  transported  in  one 
three-ton  truck. 

Lacking  the  standard  equipage,  almost  any  kind  of  boats,  rafts,  casks, 
or  in  fact  anything  that  will  float,  may  be  utilized  as  supports  for  an  impro- 
vised bridge. 

The  heavy  equipage  has  the  advantages  of  greater  strength  and  capac- 
ity, and  less  vulnerability  to  hostile  fire.  The  light  (canvas)  equipage 
has  the  advantage  of  greater  mobility  in  transport.  The  heavy  train  is 
required  when  heavy  loads  are  to  be  carried,  when  very  swift  streams  are 
to  be  crossed,  or  when  the  bridge  must  resist  ice  and  drift,  or  stand  up 
under  hostile  fire. 

The  erection  of  the  ponton  bridge  takes  the  form  of  a  drill,  and  is  accom- 
plished in  an  incredibly  short  period  of  time  by  men  who  have  been  properly 
instructed.  The  equipage,  moreover,  is  so  simple  that  average  soldiers 
may  be  quickly  trained  to  install  it. 

There  is  no  stream  too  wide,  too  deep,  or  too  swift  for  the  ponton  equip- 
age, when  handled  by  trained  men.  As  an  indication  of  its  capacity, 
adaptability,  and  speed  of  erection,  the  following  historical  examples 
will  be  of  interest. 

On  June  15th,  1864,  Gen.  Grant,  in  his  attack  on  Richmond,  had 
need  of  a  crossing  of  the  James  River.  The  stream  was  deep,  and  so  swift 
that  the  pontons  could  not  be  held  by  their  own  anchors,  it  being  necessary 
to  attach  their  cables  to  schooners  placed  in  the  stream.  The  crossing  was 
over  2,000  ft.  wide,  101  heavy  pontons  being  employed,  and  was  com- 
pleted in  5^  hours,  or  at  an  average  speed  of  6  ft.  per  minute. 

In  February,  1862,  a  bridge  of  60  boats  was  thrown  across  the  Potomac 
at  Harper's  Ferry.  The  river  was  in  flood — a  perfect  torrent — carrying 
great  quantities  of  ice  and  drift.  In  spite  of  all  these  difficulties,  the  struc- 
ture was  successfully  completed  in  8  hours — average  speed  of  erection,  2| 
ft.  per  minute. 

In  the  winter  of  1919  a  ponton  bridge  was  built  across  the  Chattahoo- 
chee River  at  West  Point,  Ga.,  by  a  detachment  of  the  7th  Engineers  with 
civilian  assistants.  The  bridge  was  reinforced  to  carry  heavy  traffic,  and 
the  flooring  was  spiked  in  place.  It  was  installed  during  a  flood,  the 
current  varying  from  5  to  10  miles  per  hour,  and  the  water  level  rising  4  ft. 
during  construction.  The  length  was  440  ft.;  and  the  bridge  was  com- 
pleted in  10  hours'  working  time. 

These  performances  under  service  conditions,  remarkable  as  they  be, 
are  quite  eclipsed  by  the  exhibition  bridge  constructed  across  the  Rhine 
(near  Honningen)  by  the  1st  Engineers,  American  Expeditionary  Forces, 
during  the  military  occupation  of  Germany  (1919).     The  river  at  this 


472  ECONOMICS   OF   BRIDGEWORK  Chapter  XLIV 

point  is  1,450  ft.  wide,  with  a  maximum  depth  of  25  ft.  and  a  current  of  3  to 
4  miles  per  hour.  The  bridge  was  built  from  both  ends,  400  trained  men 
being  employed,  and  93  pontons  (of  the  German  equipage)  being  used. 
The  structure  was  completed  in  the  astonishing  time  of  41  minutes  8  sec- 
onds, or  at  an  average  rate  of  more  than  thirty-five  feet  per  minute,  the 
world's  record  for  speed  in  bridge  construction. 

No  other  type  of  bridge  ever  devised  is  capable  of  anything  approach- 
ing such  speed  in  erection.  By  contrast  with  the  time  required  in  the  cases 
mentioned,  one  of  the  best  examples  of  the  construction  of  a  heavy,  miU- 
tary  trestle-bridge  was  a  structure  built  over  the  Little  Pedee  River  in  the 
Civil  War,  in  which  a  length  of  100  ft.  was  completed  in  about  9  hours. 

The  ponton  bridge  is  designed  to  meet  emergencies;  and  if  the  crossing 
is  to  be  required  for  any  considerable  period,  the  ponton  equipage  should 
be  released  by  the  construction  of  a  fixed  bridge,  in  order  that  it  may  be 
available  for  fresh  emergencies.  For  the  requirements  of  a  moving  column 
in  a  theatre  where  stream  crossings  are  encountered,  the  ponton  equipage 
is  indispensable.  In  addition  to  its  use  for  bridging,  the  equipage  may  also 
be  employed  for  ferrying,  as  in  the  passage  of  a  stream  by  force  in  the 
face  of  the  enemy. 

If  it  be  necessary  to  employ  the  ponton  bridge  for  a  considerable  period, 
the  chess  (floor  plank)  should  be  protected  by  a  sheathing  of  thin  lumber  or 
by  hay  or  brush.  These  chess  are  very  thin  (1|  in.),  and,  if  unprotected, 
would  soon  be  worn  through  and  ruined  by  continued  traffic. 

As  just  stated,  the  floating  equipage,  if  available,  will  often  be  the  first 
solution  for  an  important  emergency  crossing.  Subsequently,  and  as  soon 
as  possible,  it  should  be  replaced  by  a  trestle  bridge,  which  in  turn  may  later 
be  used  as  falsework  for  a  more  elaborate  structure. 

The  adaptability  of  the  ponton  equipage  is  very  great;  it  is  ideally  fitted 
to  meet  military  emergencies;  and  its  value  as  a  saver  of  time  cannot  be 
over-estimated. 

New  Types  of  Ponton  Equipage 

The  old  types  of  ponton  bridge,  which  have  so  long  served  military 
needs,  and  which  are  of  generally  similar  design  in  all  armies,  like  other 
former  types  of  military  bridges  are  inadequate  to  the  needs  of  modern 
traffic.  In  future  wars  a  heavier  equipage  will  be  required,  and  even  this 
must  be  capable  of  "reinforced"  construction  to  carry  the  augmented 
loads.  Such  an  equipage  has  been  designed  for  the  American  Army.  The 
pontons  have  an  available  buoyancy  of  10  tons,  the  span  has  been  decreased 
to  15  ft.  and  heavier  balk  are  used.  An  alLmetal  boat,  or  one  of  metal 
sheathing  on  a  wooden  frame,  will  be  employed.  The  adjustable  trestles 
for  end  spans  will  be  of  steel.  This  bridge  will  normally  cai-ry  a  concen- 
trated load  of  13,500  lbs.  on  one  axle,  and  may  be  reinforced  to  carry  an  axle 
load  of  20,000  lbs.  This  will  take  all  the  loads  of  a  corps  or  army,  except- 
ing only  heavy  tanks  and  the  guns  and  tractors  of  the  artillery  weighing 


ECONOMICS    OF   MILITARY    BRIDGES  473 

more  than  twenty  tons.  The  reinforcement  consists  of  an  intermediate 
roadway-bearer  supported  by  the  heavy  side  rails.  The  wagons  used  to 
transport  the  new  equipage  will  be  such  that  they  can  be  hauled  by  animals, 
truck,  or  tractor. 

Railroad  Bridges 

In  the  construction  of  railroad  bridges,  military  practice  follows  civil 
practice  more  closely  than  in  highway  bridges.  As  they  must  usually 
carry  heavier  loads,  and  as  variations  in  either  horizontal  or  vertical  align- 
ment are  much  more  serious,  greater  attention  should  be  paid  to  the  solidity 
of  the  structure,  including  its  foundations.  Pile  trestles,  girders,  and 
trusses  on  piers  of  pile  clusters  are  the  usual  types  of  military-railroad 
bridge.  Most  of  them,  except  for  light,  narrow-gauge  railways,  will  be  in 
rear  of  the  combat  zone,  though  often  bridges  for  standard  gauge  must  be 
constructed  close  to  the  front. 

Foot-Bridges 

Foot-bridges,  employed  usually  to  meet  tactical  emergencies,  exhibit  a 
greater  variety  of  forms,  and  have  heretofore  been  less  subject  to  standardi- 
zation than  either  vehicle  or  railroad  bridges.  In  a  crisis,  any  design  and 
any  material  that  will  serve,  or  even  partially  serve,  the  purpose  must  be 
employed.  Trees,  cut  near  the  bank  and  allowed  to  fall  across  the  stream, 
often  have  enabled  a  combatant  force  to  meet  a  grave  emergency.  As 
traffic  accidents  thereon  will  be  less  serious  than  in  the  case  of  other 
bridges,  less  attention  is  usually  paid  to  the  factor  of  safety.  If  this  be 
very  uncertain,  the  bridge  should  be  tested  by  sending  a  few  men  across, 
and  the  traffic  should  be  regulated  to  prevent  crowding. 

The  demands  for  the  rapid  passage  of  foot  troops  over  streams  are 
so  frequent  and  insistent  in  modern  warfare,  that  it  is  certain  that  in  future, 
even  more  than  in  the  past,  standardized,  portable  foot-bridges  will  form 
part  of  the  equipment  of  combatant  organizations.  A  number  of  such 
standardized  foot-bridges,  including  the  light  ponton  type  heretofore  de- 
scribed, were  devised  during  the  World  War.  Floating  types  will  be  the 
ones  most  commonly  employed,  these  being  supplemented  by  light  sectional 
trusses  and,  in  some  instances,  by  suspension  bridges.  The  floats  which 
have  been  successfully  used  include  light  canvas  pontons,  casks  of  wood 
or  steel,  rafts  of  wood  or  cork,  and  Kapok  Rafts.  The  latter  have  the 
advantage  that  they  are  unsinkable  by  rifle  or  machine-gun  fire. 

The  width  of  the  roadway  or  path  of  foot-bridges  is  from  2  to  2|  ft.  A 
greater  width  is  unnecessary  for  the  passage  of  men,  and  unduly  decreases 
the  mobility  of  the  equipage,  which  is  an  essential  requirement.  Such  a 
width  (2  ft.)  does  not  permit  the  passage  of  machine  gun  carts,  which  must 
seek  other  means  of  crossing.  Machine  guns,  light  mortars,  and  one-pound 
cannon  accompanying  the  infantry,  with  their  ammunition,  may  be  carried 
across  by  hand. 


474  ECONOMICS   OF  BRIDGEWOEK  Chapter  XLIV 

Deck  or  Flooring  of  Military  Bridges 

Dimensioned  lumber,  never  less  than  2  inches  thick  and  preferably  4 
to  5  inches  (except  for  foot-bridges),  is  most  desirable  for  decking.  The 
construction  of  a  deck  of  poles  is  a  slow  process;  because  it  is  a  tedious 
task  to  collect  and  prepare  sufficient  material  for  a  bridge  of  considerable 
length.  Poles  for  decking  should  be  at  least  3^  inches  in  diameter.  They 
should  be  well  spiked  so  that  they  will  not  rattle.  As  a  pole  deck  is 
usually  very  rough,  it  will  generally  be  advisable  to  chink  the  openings  and 
cover  first  with  brush  and  leaves  and  then  with  a  layer  of  earth.  The  addi- 
tional dead  load  thus  brought  upon  the  structure  should  not  be  overlooked. 

Woven-brush  mattresses,  supported  on  deck  poles  at  relatively  wide 
intervals  and  covered  with  earth,  make  a  satisfactory  deck  for  foot-bridges. 

The  wear  on  decking  resulting  from  military  traffic  is  very  great,  hence 
light  material  is  unsatisfactory.  For  heavy  bridges  on  important  routes  a 
deck  5  inches  thick,  preferably  of  hardwood,  is  now  regarded  as  standard. 
If  only  2-inch  material  is  available,  a  double  thickness  should  be  used.  The 
distance  between  stringers  in  feet  should  not  be  more  than  the  thickness  of 
the  decking  in  inches. 

Width  of  Roadway 

As  the  amount  of  material  and  the  time  required  for  construction 
increase  with  the  width  of  the  roadway,  military  bridges  are  made  no  wider 
than  necessary,  and  are  generally  limited  to  a  single  line  of  traffic,  with 
clearance  for  the  passage  of  footmen,  horsemen,  or  motor-cycles.  As  mih- 
tary  traffic  usually  moves  in  trains  and  can  be  closely  regulated,  it  requires 
a  less  width  of  roadway  than  unregulated  civil  traffic.  For  the  standard 
bridges,  a  roadway  of  10  or  11  feet  is  employed.  If  it  be  necessary  to  pro- 
vide for  the  continuous  movement  of  traffic  in  both  directions,  two  bridges 
side  by  side  may  be  adopted;  or,  if  the  traffic  be  very  dense,  three  or  four 
parallel  bridges  may  be  built.  Two-way  bridges  are,  of  course,  also 
employed.  A  15  ft.  roadway  will  pass  two  lines  of  traffic,  but  can  hardly 
be  called  ample  for  the  purpose,  a  width  of  18  or  20  feet  being  better. 

The  maximum  capacity  of  military  bridges  in  service  should  be  devel- 
oped by  efficient  traffic  control. 

Side-Rails  and  Hand-Rails 

Side-rails  or  wheel-guards  of  ample  strength  should  never  be  omitted 
from  any  vehicle  bridge.  Hub-guards  and  hand-rails  are  generally  pro- 
vided for  through-truss  spans,  including  suspension  bridges,  largely  for 
the  protection  of  the  bridge  itself;  l:)ut  they  ai'c  generally  omitted  in  the 
case  of  deck  spans.  On  the  other  hand,  side-rails  are  unnecessary  for 
foot  bridges,  except  to  secure  the  flooring;  but  hand-rails  are  generally 
provided. 

Materials  Em-ployed,  in  Military  Bridging 

Any  available  material  must  be  utilized  in  the  construction  of  military 


ECONOMICS   OF   MILITARY   BRIDGES  475 

bridges.     Even  bamboo  has  been  successfully  employed  to  carry  heavy 
loads. 

Timber 

Timber  can  be  adapted  to  the  requirements  of  bridge  construction  more 
easily  and  rapidly  than  any  other  material.  It  is  also  the  most  generally 
available  of  all  bridge  materials.  For  civil  constructions  it  has  the  dis- 
advantage of  lack  of  permanence — a  consideration  having  little  or  no 
weight  in  military  operations. 

Timber,  accordingly,  is  the  favorite  material  of  the  military  bridge 
builder.  Dimensioned  (sawed)  timber  is  greatly  preferable  to  round  timber 
(unsawed  logs  and  poles) ;  first,  because  it  can  be  much  more  quickly  incor- 
porated in  the  bridge;  second,  because  it  makes  a  stronger  and  better  struc- 
ture; and  third,  because  it  lends  itself  better  to  standardized  designs  and 
methods  of  construction.  A  few  standard  sizes  of  lumber  (sawed  timber), 
sufficient  to  meet  the  requirements  of  the  standardized  designs,  are  prefer- 
able to  a  great  number  of  miscellaneous  sizes  that  are  difficult  to  adapt  to 
any  design. 

Military  bridges  must  be  and  are  frequently  constructed  of  round 
timber,  but  this  is  from  necessity  and  not  from  choice.  Round  timber  is 
seldom  used  (except  for  piles  or  posts  of  framed  trestles),  if  dimensioned 
material  is  available. 

Piling 

Piles  are  frequently  employed  for  abutments,  trestles,  and  piers  in 
situations  where  the  nature  of  the  bottom  does  not  permit  the  use  of  framed 
trestles.  The  use  of  piles  necessitates  a  pile-driver,  and  consequently  at  the 
front  should  be  avoided  if  possible,  although  frequently  necessary  there. 
Framed  trestles,  which  require  no  plant  for  their  erection,  are  preferable, 
even  if  it  be  obligatory  to  rip-rap  the  bottom  in  order  to  increase  its  bearing 
power,  or  to  prevent  scour.  Nevertheless  there  will  be  situations,  even  at 
the  front,  where  piles  must  be  used ;  and  portable  pile-drivers  will  be  a  part 
of  the  engineer  equipment  of  every  army. 

Steel 

Any  steelwork  which  involves  field  riveting  will  find  little  application  in 
mihtary  bridging,  even  on  the  lines  of  communication,  for  the  reason  that 
its  erection  demands  special  plant  and  skilled  labor.  Rolled  sections 
(I-Beams)  are  frequently  employed  as  stringers  in  trestle  bridges  on  the 
lines  of  communication,  and  even  at  the  front,  when  it  is  necessary  to  carry 
very  heavy  loads,  such  as  tanks. 

Portable,  demountable,  steel  truss-bridges,  capable  of  very  rapid 
erection,  and  designed  for  both  light  and  heavy  traffic,  were  employed  in 
the  World  War.  The  designs  were  very  ingenious,  and  such  structures  will 
undoubtedly  be  used  to  a  great  extent  in  future. 

Special  fabricated-steel  girders  are  frequently  employed  for  long  stringer- 


476  ECONOMICS   OF  BRIDGEWORK  Chapter  XLIV 

spans,  mainly  for  railroad  bridges  on  the  Knes  of  communication.  Their 
purpose,  of  course,  is  to  reduce  the  time  required  for  pier  construction. 
They  differ  in  no  essential  from  civil  structures  for  similar  situations. 

Concrete 

Concrete  is  utihzed  for  culverts,  for  foundations  of  framed  trestles, 
occasionally  for  abutments  of  bridges  on  important  routes  of  communica- 
tion, and  in  the  repair  of  old  masonry  bridges.  For  piers,  piHng  or  crib- 
work  is  almost  invariably  preferable,  even  in  the  case  of  large  and  important 
bridges.  Arches  and  girder  spans  of  concrete  will  seldom  be  used.  In  the 
battle  zone  concrete  finds  very  little  application  in  bridgework. 

Stone 

Stone  is  employed  as  rip-rap  for  the  protection  of  piers  and  abutments, 
and  as  crib-filling.  Stone  masonry  will  only  exceptionally  be  used  for 
abutments  or  wing  and  retaining  walls;  for  there  will  be  but  few  situations 
in  which  either  concrete  or  rubble-concrete  would  not  be  preferable.  If  no 
cement  is  available,  lime-mortar  or  dry-stone  walls  are  sometimes  employed. 

Paint 

Paint  and  other  protective  materials  are  sparingly  used  in  military 
bridging.  Ordinarily  the  time  for  which  the  structures  will  be  required 
does  not  justify  the  employment  of  these  preservatives.  Steelwork  should 
always  receive  a  shop  coat,  but  field  coats  will  usually  be  omitted. 

Joints  and  Fastenings 

As  military  bridges  must  be  constructed  in  the  least  possible  time  and 
usually  by  unskilled  labor,  intricate  joints,  involving  expert  carpentering, 
are  to  be  avoided.  Generally  a  plain  butt  joint,  requiring  no  carpentering, 
other  than  squaring  the  end  of  a  timber,  should  be  used.  The  fastenings 
ordinarily  employed  for  hasty  bridges  include  lashings  of  rope,  marline,  or 
wire;  dogs;  fish-plates  or  " scabbing " ;  drift  bolts;  through  (screw)  bolts; 
and  spikes. 

Lashings  are  employed  in  the  absence  of  other  materials,  or,  as  in  the 
floating  equipage  (which  is  generally  lashed  throughout),  when  the  bridge  is 
to  be  later  dismantled  and  the  material  salvaged.  They  are  not  a  very 
secure  form  of  attachment,  especially  when  they  actually  carry  the  load, 
as  in  the  case  of  the  cap  of  a  spar  trestle.  In  such  structures  it  is  advisable 
to  dap  or  notch  the  timbers  together.  Marline  gives  a  tighter  lashing 
than  rope,  but  not  such  a  strong  one;  and  small  rope  is  profoiable  to  large. 
Lashings  do  not  stand  racking  well,  and  often  are  not  sufficiently  durable 
even  for  military  uses. 

Dogs  are  easily  made  of  any  iron  available.  They  should  not  ho  em- 
ployed to  carry  a  load,  but  only  to  hold  timber  in  position. 

Drift  bolts  are  commonly  employed  as  fastenings  for  all  ])arts  of  a  bridge 
except  the  deck.     They  are  readily  made  up  in  any  desii-ed  length,  and  are 


ECONOMICS   OF  MILITARY  BRIDGES  477 

quickly  driven.  A  variation  in  the  length  of  the  bolt  makes  no  difference, 
provided  it  is  long  enough.  It  is  not  necessary  to  point  the  ends.  Lag 
screws  may  be  used,  if  available. 

Through  bolts,  with  nuts  and  washers,  are  the  most  secure  form  of 
fastenings;  and,  if  procurable,  they  should  be  used  for  all  important  joints, 
except  sills  and  caps  which  are  usually  "riders"  (butted  on  the  trestle 
legs),  and  for  which  drift  bolts,  dogs,  or  scabbing,  are  employed.  For 
round  timbers,  through  bolts  have  the  disadvantage  that  they  are  generally 
either  too  long  or  too  short,  requiring  the  use  of  wooden  washers  in  one  case, 
or  dapping  out  the  timber  in  the  other — in  either  instance  involving  a  loss 
of  time.  Turned  bolts  are  invariably  used  in  lieu  of  field  rivets  in  the  assem- 
bly of  sectional  steel  trusses. 

A  full  supply  of  nails  and  spikes  of  assorted  sizes  should,  of  course,  be 
provided. 

Sizes  of  Individual  Members 

For  bridges  at  the  front,  the  sizes  of  individual  members  must  gen- 
erally be  such  that  they  can  be  readily  handled  and  placed  by  unskilled 
labor,  with  the  aid  of  animals  and  ordinary  tackle,  gin-poles,  or  shears. 
In  the  cases  when  plant  is  available,  heavier  pieces  may  be  used  to  advan- 
tage. The  principal  considerations  limiting  the  size  of  individual  pieces 
are  the  requirements  of  transportation,  by  motor  truck  as  well  as  by  rail. 

Plant  and  Tools 

The  mihtary  bridge  builder  in  the  past  has  made  comparatively  little 
use  of  heavy  construction  plant  in  his  operations,  but  this  resulted  from 
necessity  rather  than  choice.  Construction  plant  is  utilized  whenever 
practicable;  and  in  view  of  the  great  capacity  now  required  of  military 
bridges,  portable  plant  is  necessary  even  in  the  combat  zone.  However,  in 
the  tactical  operations  of  the  combat  troops  the  opportunities  for  the 
emplo3Tiient  of  plant  will  be  relatively  few.  The  work  of  the  military 
bridge  builder  is  spread  over  a  considerable  area;  he  moves  rapidly  from 
place  to  place;  and  he  cannot  be  unduly  hampered  in  his  movements  by  the 
necessity  of  transporting  heavy  construction  plant.  Usually  the  plant  is 
not  at  hand  when  needed,  and  it  can  seldom  be  depended  upon.  More- 
over, one  of  the  principal  uses  of  plant  is  to  save  manual  labor,  and  this 
consideration  has  less  weight  in  military  than  in  civil  constructions. 

There  are,  however,  a  number  of  pieces  of  light,  portable  construction- 
plant  that  may  often  be  advantageously  employed,  even  at  localities 
quite  close  to  the  front.  These  include  small  hoists,  pile-drivers,  com- 
pressors, pneumatic  tools,  concrete  mixers,  and  rock  crushers.  Gasoline 
is  the  best  motive  power,  because  of  the  compactness  of  both  machine  and 
fuel.  For  works  on  the  lines  of  communication;  heavy,  standard  construc- 
tion-plant is  frequently  adopted.  For  the  future,  portable  hoists  and 
pile-driving  outfits  will  be  provided  for  corps  and  army  engineer-troops. 


478  ECONOMICS   OF  BRIDGEWORK  Ch.\pter  XLIV 

The  tools  used  in  military  bridge  work,  like  the  structures  built  there- 
with, should  be  of  the  utmost  simpUcity.  There  should  be  an  ample  supply 
of  the  common  tools,  such  as  picks,  mattocks,  axes,  saws,  hammers, 
wrenches,  shovels,  cant-hooks,  etc.,  with  a  few  of  the  less  usual  tools  that 
will  occasionally  be  required.  AU  should  preferably  be  of  commercial  sizes; 
but,  to  meet  emergencies,  miniature  ■  tools,  easily  transported  on  a  pack 
mule  or  on  the  person  of  the  soldier,  should  also  be  available  in  case  of 
need.  There  will  arise  situations  in  which  the  entire  equipment  of  the 
bridge  builder  must  be  carried  on  pack  mules. 

Class  of  Labor  Available 

Mihtary  bridges  must  usually  be  built  chiefly  by  unskilled  labor.  In 
every  engineer  organization  there  wiU  be  a  number  of  skilled  artisans  of 
every  class;  but  the  majority  of  the  men  in  the  ranks  of  these  organiza- 
tions, as  well  as  those  from  labor  battalions  and  working  parties  from  the 
infantry,  wiU  be  of  the  class  known  as  "unskilled  labor."  This  fact  has  an 
important  bearing  on  the  design  and  methods  of  construction  of  mihtary 
bridges. 

Improvisation  and  Standardization. 

The  difficult  situations  encountered,  the  varied  circumstances  under 
which  work  must  be  performed,  the  emergencies  constantly  arising,  and  the 
necessity  of  adapting  to  his  purposes  whatever  materials  are  available,  will 
require  the  military  bridge  builder  to  be  skilled  in  improvising  struc- 
tures to  meet  these  conditions.  Improvisation,  in  fact,  is  characteristic 
of  all  the  operations  of  military  engineering.  It  is  a  valuable  means  of 
developing  ingenuity  and  resourcefulness;  nevertheless  it  is  a  practice  which 
results  only  from  necessity,  and  it  has  the  disadvantages  that  it  consumes 
valuable  time  and  that  it  tends  towards  lack  of  uniformity  both  in  training 
and  in  actual  construction. 

Standardization,  including  standard  designs,  standard  materials,  and 
standard  methods  of  construction  and  of  training,  is  at  least  as  useful  and 
economical  in  military  practice  as  in  civil  practice.  It  has  the  follow- 
ing important  military  advantages: 

(a)  A  standardized  structure  can  always  be  erected  in  less  time  than 
one  in  which  extensive  improvisation  is  necessary,  especially  by  troops  who 
have  been  trained  in  standardized  construction.  The  saving  of  time  results 
from  both  the  fact  that  it  is  possible  to  use  standard  plans,  and  that  loss  of 
time  from  improvisation  is  eliminated. 

(6)  A  further  saving  of  time  is  effected  by  the  fact  that  standardized 
materials  may  be  prepared  beforehand  at  the  engineer  depots,  and  sent  to 
the  front  as  needed.  Lumber  can  be  cut  to  exactly  the  required  dimensions, 
bolts  will  be  of  exactly  the  i-ight  length,  and  special  pieces  of  all  kinds  can 
b(;  made  up  in  rear,  so  that  it  will  not  be  necessary  to  spend  time  in  pre- 
paring them  under  difficult  conditions  at  the  front. 


ECONOMICS   OF   MILITARY   BRIDGES  479 

(c)  Standardized  structures  require  less  skilled  labor  than  improvised 
structures. 

(r/)     Standardization  promotes  imiformity  in  training  and  practice. 

(e)  A  standardized  structure  is  nearly  always  superior  to  an  improvised 
structure  in  every  item  of  utility. 

(/)  In  a  hasty,  improvised  bridge  constructed  of  random  materials,  the 
actual  strength  of  the  structure  is  usually  a  matter  of  uncertainty  and 
guess-work.  In  standardized  designs  the  safe  loading  is  accurately  known, 
and  the  chance  of  accident  from  overloading  the  structure  is  correspond- 
ingly reduced. 

The  benefits  of  standardization  being  so  manifest,  standardized-type 
plans  have  been  prepared  for  all  forms  of  military  bridges,  even  for  those 
constructed  of  local  materials.  Standardized  material  for  these  structures 
is  prepared  in  the  engineer  shops,  so  as  to  reduce  as  far  as  possible  the 
amount  of  labor  required  in  the  field.  Standardized  designs  are,  or  should 
be,  of  the  utmost  simplicity  and  flexibility.  They  should  be  simple, 
because  only  the  simplest  structures  can  be  successfully  and  promptly 
erected  under  the  difficult  conditions  incident  to  warfare,  involving  lack  of 
time,  adequate  tools  and  plant,  skilled  labor,  etc.  They  should  be  flexible, 
because  no  two  situations  are  exactly  alike;  and  the  type  plans  must  be 
modified  in  practice  to  meet  the  actual  conditions.  It  should  be  possible, 
with  a  few  minor  variations,  to  adapt  the  type  plans  and  the  standard 
materials  to  any  situation,  with  a  minimum  of  improvisation.  The  best 
example  of  standardization  in  military  bridging  is  the  sectional  steel  truss 
heretofore   described. 

It  has  been  said  that  standardization  has  a  tendency  to  discourage 
invention,  and  hence  is  inimical  to  progress.  While  it  must  be  admitted 
that  there  is  some  truth  in  this  contention,  the  tremendous  results  that 
have  been  achieved  through  standardization,  in  both  civil  and  military 
practice,  are  a  sufficient  justification  for  its  adoption.  There  will  be  an 
ample  field  for  the  inventive  talents  and  resourcefulness  of  the  engineer, 
both  within  and  without  the  limitations  imposed  by  standardization. 
Moreover,  for  every  inventive  genius  who  has  been  discouraged  by  stand- 
ardization there  are  thousands  of  average  men  who  have  profited  by  it; 
and  it  is  the  average  man  with  whom  we  invariably  reckon  in  military  oper- 
ations of  all  kinds.  Standards  should  be-  revised  and  improved  in  the 
light  of  experience;  and  this  was  frequently  done  during  the  World 
War. 

Because  of  the  density  of  traffic  and  the  heavy  loads  incident  to  modern 
military  operations,  standardized  bridge  designs  will  be  employed  more 
frequently  in  the  future  than  they  have  been  in  the  past.  There  were 
times  during  the  World  War  when  the  regular  daily  traffic  on  a  single  road 
was  5000  motor  trucks  (in  both  directions),  and  during  troop  movements 
this  reached  a  maximum  of  more  than  17,000.  Rough,  improvised  struc- 
tures would  not  be  adequate  to  the  needs  of  such  a  traffic. 


480  ECONOMICS   OF  BRIDGEWORK  Chapter  XLIV 

Utilization  of  Existing  Bridges 

To  save  time,  material,  and  labor  and  to  obtain  quicker  results,  existing 
bridges  should  always  be  utilized  as  far  as  possible.  Unless  the  bridge  is  a 
complete  wreck,  it  will  nearly  always  be  easier  to  repair  or  strengthen  it 
than  to  build  a  new  structure.  Existing  bridges  should  be  examined  by 
an  engineer  who  is  familiar  with  bridge  construction  in  the  particular 
locality.  Any  bridge  built  on  approved  standard  design,  and  the  parts  of 
which  are  in  good  condition,  may  be  regarded  as  safe  for  its  rated  loading. 
Any  bridge  that  exhibits  a  radical  departure  from  standard  design  should, 
of  course,  be  looked  upon  with  suspicion.  The  horizontal  and  vertical 
ahgnments  of  the  structure  should  be  noted,  after  which  all  its  parts  should 
be  examined  for  weakness  or  deterioration.  The  conduct  of  the  bridge  as 
loads  pass  over  it  should  be  carefully  observed. 

A  weak  bridge  of  any  type  may  be  strengthened  by  placing  additional 
trestle  bents  between  its  supports,  or  by  strutting  its  stringers.  All  bracing 
should  be  thoroughly  reinforced.  Even  in  the  case  of  a  demolished  bridge, 
it  will  generally  be  possible  to  utihze  at  least  its  abutments  and  piers,  or 
what  remains  of  them.  A  fallen  truss  may  often  be  raised  to  position  and 
its  undamaged  portion  made  available  by  introducing  a  new  pier.  A 
few  hours'  work  will  often  render  a  weak  bridge  sufficiently  strong  to  carry 
military  loads;  whereas,  if  it  be  allowed  to  break  down,  extensive  recon- 
struction or  even  a  new  bridge  may  be  needed.  It  certainly  is  a  very  poor 
bridge  indeed  that  cannot  be  strengthened  sufficiently  to  carry  the  desired 
loads,  with  less  labor  than  would  be  required  to  build  a  new  structure; 
and,  in  the  interests  of  economy,  such  strengthening  should  always  be 
undertaken. 

Utilization  of  Local  Resources 

To  save  transportation,  to  promote  mobility,  and  to  meet  the  frequent 
emergencies  in  which  no  standard  materials  will  be  available,  the  military 
engineer  will  often  have  occasion  to  build  his  bridges  of  any  local  materials 
that  may  be  available.  Structures  built  of  such  materials  are  generally 
known  as  hasty  or  improvised  bridges.  While  the  utilization  of  local 
resources  may  save  transportation,  it  will  not  economize  time  in  construc- 
tion. A  great  deal  of  time  and  effort  must  usually  be  expended  in  finding 
and  collecting  the  available  material,  and  in  transporting  it  to  the  site  of 
the  work;  and  when  it  is  there,  further  difficulty  will  be  encountered  in 
adapting  the  heterogeneous  collection  to  the  standard  clesigns,  oi-  indecnl 
to  any  design 

In  a  wooded  area,  round  timber  will  be  available,  and  will  jirove  io  bo 
very  satisfactoi-y  for  the  (construction  of  bridges,  though  by  no  moans  equal 
to  sawed  lumber  of  standard  sizes.  As  before  stated,  the  military  engineer 
does  not  use  round  timber  from  choice,  although  it  may  be  remarked  that 
bridges  constru(ctod  of  such  niatcM'ial  hav(^  a  characteristically  military  ap- 
pearance, and  sometimes  a  certain  rustic  beauty  quite  jik^asing  to  the 


ECONOMICS   OF  MILITARY   BRIDGES  481 

eye.  But  it  is  also  to  be  remarked  that  it  was  to  ayoid  the  loss  of  time 
involved  in  laboriously  collecting  the  material  for  and  constructing  such 
bridges,  that  the  ponton  equipage  and  the  standard  types  of  fixed  bridges 
were  devised.  The  construction  of  a  bridge  of  round  timber  is  a  rather 
entertaining  recreation,  and  engineers  occasionally  overlook  the  loss  of 
time  thus  involved;  hence  it  should  be  avoided  whenever  possible.  The 
collection  of  the  material  and  the  laying  of  a  pole  deck,  in  particular,  con- 
stitute a  time-consuming  operation.  In  building  a  bridge  of  mixed  mate- 
rial, the  round  timber  may  be  employed  for  trestle  posts,  sills,  and  caps, 
and,  if  necessary,  also  for  stringers  and  side  rails,  leaving  the  dimensioned 
stuff  for  bracing,  stringers,  and  deck — especially  the  deck. 

In  almost  every  town,  unless  it  has  been  previously  overrun  by  the 
military,  a  small  stock  of  lumber  can  be  found;  and  frame  buildings  may  be 
wrecked,  if  necessary.  This,  in  combination  with  standing  timber,  will 
often  meet  the  needs  of  the  situation.  Local  materials  are,  in  general, 
decidedly  inferior  in  all  respects  to  standardized  materials  from  the  engineer 
depots.  They  must,  however,  frequently  be  employed;  and  the  engineers 
should  be  skilful  in  collecting  them  and  in  adapting  them  to  their  needs. 

Loading  of  Military  Bridges 

The  military  bridge  builder  should  be  familiar  with  the  usual  loads 
that  bridges  in  various  situations  and  for  various  purposes  will  be  called 
upon  to  bear.  Usually  these  loads  are  quite  definite,  and  the  standardized 
designs  are  based  upon  them.  As  the  factor  of  safety  employed  in  military 
bridging  is  almost  always  low,  especially  at  the  front,  vehicles  heavier  than 
those  for  which  the  structure  was  designed  should  not  be  permitted  to 
cross  it.  Nevertheless,  it  is  generally  unpossible  to  foresee  the  extent 
to  which  any  bridge  may  be  used.  Bridges  on  important  routes  of  trans- 
port are  almost  certain  to  be  called  upon  to  carry  the  heaviest  loads. 
Drivers  of  heavy  trucks  wiU  proceed  across  any  bridge  they  come  to,  what- 
ever warning  signs  may  be  posted,  unless  a  guard  is  placed  at  the  structure. 

Accordingly,  it  is  desirable  that,  on  any  main  route,  or  any  road  apt  to 
become  an  important  route,  the  bridges,  whatever  their  immediate  purpose, 
should  be  built  to  carry  the  heaviest  mihtary  loads.  The  supports,  at 
least,  should  be  made  of  ample  strength,  which  will  allow  the  bridge  later 
to  be  reinforced  to  carry  heavy  loads  by  introducing  additional  supports 
or  otherwise  strengthening  the  superstructure. 

In  general,  the  first  crossing  will  be  a  hasty  improvisation,  or  a  light 
foot-bridge  of  some  standard  design.  If  the  need  for  the  crossing  continues, 
this  bridge  may  be  replaced  by  the  ponton  equipage,  and  subsequently  by 
an  improvised  or  standardized  fixed  bridge.  By  this  time  the  probable 
future  needs  of  the  route  will  be  known  with  some  certainty,  and  future 
steps  can  be  taken  accordingly. 

There  should  be  an  ample  number  of  through  routes  having  bridges 
capable  of  carrying  the  greatest  loads,  including  tanks  and  heavy  artillery. 


482  ECONOMICS   OF   BRIDGEWORK  Chapter  XLIV 

These  routes  for  heavy  traffic  should  be  properly  sign-posted ;  and  informa- 
tion concerning  them  should  be  circulated  throughout  the  command.  It 
will  evidently  be  impossible  to. provide  all  routes  with  the  heaviest  bridges; 
hence  a  rigid  traffic  supervision  should  be  exercised  to  prevent  heavy 
vehicles  from  wandering  into  the  minor  routes  where  the  bridges  have  not 
sufficient  strength  to  carry  the  loads  that  would  thus  be  imposed  upon  them. 

The  foregoing  requirements  conflict  to  some  extent  with  the  previous 
statement  that  a  hasty  bridge  should  be  built  with  a  low  factor  of  safety 
and  to  meet  the  exigency  of  the  moment  only.  •  Most  bridges  constructed  for 
tactical  uses  will  be  off  the  main  routes  of  transport.  In  any  case,  the 
engineer  must  decide  whether  the  probable  future  service  justifies  the 
expenditure  of  more  time  in  initial  construction. 

In  the  operations  of  the  large,  fuUy-equipped,  modern  army,  stand- 
ardized steel  superstructures,  capable  of  carrying  its  heaviest  loads,  will 
hereafter  be  characteristic  of  aU  important  routes  of  transport,  even  quite 
close  to  the  front.  In  the  operations  of  small,  detached,  rapidly-moving, 
and  lightly-equipped  forces  in  a  sparsely  settled  country,  the  fighter  forms 
of  floating  bridge,  and  various  kinds  of  improvised  structures  to  carry 
moderate  loads,  will  in  the  future,  as  in  the  past,  be  typical  of  bridging 
activities.  In  any  campaign,  miprovised  structures  will  always  be  required 
in  the  combat  zone. 

Transportation  of  Materials 

There  is  always  a  shortage  of  transportation  for  every  purpose  in  time 
of  war.  Such  important  supplies  as  ammunition,  weapons,  and  food  must 
naturally  take  precedence  over  construction  materials.  When  the  neces- 
sity for  a  bridge  can  be  foreseen  for  a  reasonable  time,  it  may  be  practicable 
to  assemble  in  advance  the  plant  and  material  requisite  for  its  erection. 
This  will  often  be  possible  on  the  lines  of  communication;  but  at  the  front 
it  will  be  absolutely  impracticable  to  have  on  hand,  at  every  locality  where 
an  emergency  may  demand  a  bridge,  all  the  materials  required  for  the 
standardized  design.  The  engineer  is  thus  compelled  to  improvise  and 
adapt  to  his  needs  such  miscellaneous  material  as  he  can  secure  on  short 
notice,  locally  or  otherwise. 

Where  military  activities  can  be  foreseen,  depots  or  "dumps"  of 
construction  material  are  assembled  in  the  vicinit}',  so  that  only  local 
transport  will  be  required.  Large,  heavy,  awkwardly-shaped  pieces  will 
always  be  delayed  in  transport.  They  are  difficult  to  load  and  ship; 
moreover,  they  arouse  the  hostility  of  the  transport  personnel,  who  have  a 
natural  tendency  to  push  them  towards  the  bottom,  of  the  "priority  list"; 
hence,  all  bridge  material  should  ])o  of  a  siz(>  and  weight  that  will  insure 
reasonable  pi'om])tness  in  transportation. 

While  it  will  s(^klom  be  possible  to  supply  \ho  engiiuHM'  with  everything 
that  he  needs,  it  will  often  be  jiracticable  to  provide  certain  materials  that 


ECONOMICS   OF   MILITARY   BRIDGES  483 

will  greatly  reduce  the  time  required  for  construction.  For  example,  the 
building  of  a  pole  floor  is  the  slowest  item  of  an  improvised  bridge.  If 
dimensioned  flooring  material  (decking)  alone  can  be  sent  up  from  the 
rear,  a  material  loss  of  time  is  elmiinated,  and  the  engineer  will  be  able  to 
improvise  the  rest  of  the  structure.  Bolts,  spikes,  wire,  cordage,  etc.,  form 
a  very  small  part  of  the  weight  of  the  bridge — they  come  in  small  packages 
and  are  easily  transported.  Without  them  the  time  and  difficulty  involved 
in  building  the  structure  would  be  greatly  increased;  hence,  these  fasten- 
ings, at  least,  should  be  made  available  wherever  needed. 

Selection  of  Site 

In  many  cases  there  will  be  little  room  for  choice  in  the  selection  of  a 
site.  New  bridges  must  frequently  be  built  at  locahties  where  former 
bridges  have  been  destroyed.  In  any  case  accessibility  to  adjacent  roads 
on  both  sides  will  be  a  controlling  factor  in  fixing  the  site,  except  for  foot- 
bridges. The  location  must  fulfill  the  tactical  requirements;  but,  as  a  rule, 
the  chief  tactical  requirement  is  rapid  construction,  and,  accordingly,  the 
site  is  selected  with  this  in  view.  Where  there  is  room  for  choice,  the 
following  conditions,  affecting  the  time  required  for  construction,  wiU  be 
given  consideration. 

(a)  Width  of  Stream.  This,  of  course,  directly  affects  the  length  of  the 
bridge  and  the  time  required  for  its  construction.  Other  things  being 
equal,  the  narrowest  point  is  preferred. 

(6)  Depth  of  Water.  The  time  and  effort  required  for  the  construction 
of  any  type  of  fixed  bridge  increases  rapidly  with  the  depth  of  water, 
unless  the  stream  can  be  crossed  with  a  single  span  (truss  or  suspension). 
For  the  ponton  bridge  there  should  be  sufficient  depth  to  float  the  boats. 
Any  greater  depth  does  not  increase  the  time  required,  except  that  very 
great  depths  make  the  anchorage  of  the  pontons  somewhat  more  difficult. 
Its  independence  of  the  depth  of  water  is  one  of  the  principal  advantages 
of  the  floating  equipage. 

(c)  Swiftness  of  Current.  A  swift  current  greatly  increases  the  diffi- 
culty of  constructing  and  maintaining  any  type  of  bridge,  except  one  with 
a  single  span  from  bank  to  bank.  The  slowest  current  is  found  in  wide, 
straight  reaches  of  the  stream. 

(d)  Nature  of  Bottom.  A  very  soft,  yielding  bottom  will  demand  pile 
or  crib  construction,  whereas  a  hard  bottom  will  support  framed  trestles, 
which  can  be  more  rapidly  placed.  A  ponton  bridge,  or  a  fixed  bridge  of  a 
single  span,  is,  of  course,  independent  of  the  nature  of  the  bottom,  as  it  is 
of  the  depth. 

(e)  Nature  of  Banks  and  Approaches.  A  low,  flat,  and  marshy  ap- 
proach, or  one  subject  to  overflow,  will  demand  either  a  very  long  bridge, 
or  a  causeway,  the  construction  of  which  is  apt  to  require  much  more  time 
than  the  bridge  itself.  .  On  the  other  hand,  high  banks  will  necessitate  tail 


484  ECONOMICS   OF   BRIDGEWORK  Chapter  XLIV 

trestles;  or  else  they  must  be  cut  down  to  provide  approaches  with  a  prac- 
ticable grade — an  operation  usually  involving  much  labor.  The  ponton 
bridge  demands  low  approaches,  as  its  height  above  the  water  surface  can- 
not be  increased.  For  crossings  of  small  or  moderate  width  that  can  be 
cleared  with  a  single  span  or  by  using  a  small  number  of  intermediate 
supports,  high  banks  will  be  no  great  disadvantage;  consequently,  for  any 
type  of  bridge,  the  most  favorable  crossing  is  one  having  low,  firm  banks 
of  equal  height,  but  above  the  level  of  any  flood  likely  to  occur  during  the 
time  that  the  bridge  is  in  use. 

(/)  Materials  Available.  If  the  bridge  is  to  be  constructed  in  whole 
or  in  part  of  materials  obtained  at  the  site,  the  availability  of  such  local 
materials,  without  an  excessive  amount  of  transportation,  is  important. 
There  are  certain  other  considerations,  of  a  tactical  nature,  that  have  a 
bearing  on  the  selection  of  a  bridge  site.  Amongst  these  may  be  men- 
tioned : 

(g)  Defensibility.  It  is  desirable  that  the  bridge  be  located  where  its 
construction  cannot  be  interfered  with  by  the  enemy,  and  where  it  and  the 
troops  crossing  it  will  not  be  subject  to  artillery  or  rifle  flre  after  its  com- 
pletion. If  built  in  the  near  presence  of  the  enemy,  it  will  be  advisable, 
before  beginning  construction,  to  ferry  some  troops  across,  in  order  to  pre- 
vent the  enemy's  snipers  from  interfering  with  the  work.  It  is  desirable 
to  locate  the  bridge  in  a  position  where  it  is  sheltered  by  woods  or  hills  from 
hostile  flre,  and  where  it  cannot  be  seen  for  any  great  distance  either  up  or 
down  stream. 

(h)  Secrecy.  If  the  crossing  is  to  be  made  secretly  as  a  surprise,  it  is 
desirable  that  there  be  a  sheltered  locality  on  the  near  bank,  at  or  close 
to  the  bridge  site,  where  the  material  can  be  assembled  without  the  enemy's 
knowledge. 

To  sum  up  then,  the  desirable  requisites  for  a  bridge  site  are:  accessi- 
bility to  adjacent  roads;  narrow  width  of  crossing;  moderate  depth  and 
swiftness  of  current;  solid  bottom;  favorable  approaches;  usually  low, 
firm  banks  of  equal  height;  materials,  as  needed,  available  near  at  hand; 
and  a  sheltered,  concealed,  and  defensible  locality. 

In  making  a  reconnaissance  for  the  selection  of  a  site,  these  various  desid- 
erata must  be  balanced  against  each  other  in  coming  to  a  decision;  for  it 
will  seldom  be  practicable  to  find  a  location  that  combines  all  the  advan- 
tages mentioned.  In  the  selection  of  a  site  for  a  railroad  bridge  there  will, 
of  course,  be  less  latitude  than  in  the  case  of  a  highway  structure.  It  is  to 
be  remembered  that  the  thing  sought  is  not  a  site  for  a  n(nv  l)ritlgo,  but  a 
practicable  crossing  of  the  stream.  A  bridge  should  not  be  built  if  a  suitable 
ford,  or  an  existing  bridge  which  meets  (or  may  b(^  mad(^  to  nuH't)  recjuire- 
ments,  can  be  found.  In  anticipation  of  their  probable  future  use,  all 
existing  bridges  within  range  of  the  army's  operations  should  be  promptly 
siezed  and  guai'ded,  in  order  to  prevent  their  destruction  by  either  the 
enemy  or  his  sympathizers. 


ECONOMICS    OF   MILITARY    BRIDGES  485 

Protection  against  Flood  and  Drift 

Military  bridges  are  protected  against  flood,  ice,  and  drift  by  the  usual 
methods  of  civil  practice.  Trestles  may  be  strengthened  against  lateral 
thrust  by  guying  upstream  or  strutting  downstream.  One  or  more  wide 
spans,  with  booms  or  guide  walls,  may  be  provided  for  the  passage  of 
ice  and  drift.  Cribs  or  clumps  of  piles  are  used  as  fenders  and  ice  breakers. 
Ponton  bridges  should  have  a  draw  span  that  may  be  removed  for  the 
passage  of  drift,  with  booms  to  guide  the  latter  into  the  opening. 

Inspection  of  Bridges 

All  the  important  bridges  in  the  area  occupied  by  an  army  should  be 
inspected  at  suitable  intervals  by  specially  qualified  engineer-officers. 
This  should  be  done  at  least  once  a  month,  and  the  results  of  the  inspection 
reported  to  the  Chief  Engineer.  At  such  inspections,  any  change  in  the 
nature  or  density  of  the  traffic  should  be  ascertained.  It  is  quite  as  impor- 
tant to  note  the  change  in  the  condition  of  the  bridge  since  the  last  inspec- 
tion, as  it  is  to  determine  its  present  condition. 


CHAPTER  XLV 


CONCLUSION 


The  devotion  of  an  entire  chapter  specifically  to  the  conclusion  of  an 
engineering  treatise  is  somewhat  of  an  innovation  in  technical  literature, 
and,  therefore,  demands  an  explanation  for  its  intrusion.  The  essential 
reason  is  that  this  is  to  be  the  author's  last  technical  book,  excepting  only 
that  after  the  third  thousand  of  his  "Bridge  Engineering,"  now  on  sale,  is 
exhausted,  he  intends  to  write  for  the  second  edition  thereof  an  "Appendix" 
to  cover  the  results  of  all  bridge  investigations,  other  than  economic,  which 
he  has  made  (or  shall  have  made)  since  that  work  was  first  issued  in  the 
summer  of  1916. 

The  reasons  why,  after  thirty-seven  years  of  rather  desultory  book- 
writing,  he  is  about  to  desert  the  field  of  technical  literature,  or,  strictly 
speaking,  that  portion  of  it  which  pertains  to  the  preparation  of  formal 
treatises,  are  the  following: 

First.  In  many  cases  the  writing  of  technical  works  is  an  extrava- 
gant indulgence  that  very  few  engineers  can  afford;  for  not  only  does 
it  necessitate  the  expenditure  of  a  large  amount  of  cold  cash  to  prepare 
the  manuscript  of  any  book  worthy  of  being  considered  real  engineering 
literature,  but,  even  after  it  is  finished,  an  author  sometimes  has  to  pro- 
vide all  the  money  required  for  publication;  the  publisher  deeming  the 
many  years  spent  and  the  great  outlay  of  money  used  in  building  up 
the  means  for  placing  such  works  on  the  market  a  fair  equivalent  for 
that  spent  in  preparing  the  manuscript.  This  is  specially  true  in  scien- 
tific books  which  require  special  means  and  careful  study  to  put  them 
properly  before  those  they  are  written  for. 

Second.  The  amount  of  personal  time  that  one  nuist  devote  to  the 
preparation  of  the  MS.  of  any  engineering  work  which  aims  to  offer  mainly 
original  material,  and  is  not,  like  many  engineering  books,  a  mere  com- 
pilation of  data  gathered  from  standard  treatises  and  the  technical  press, 
is  simply  appalling;  and  the  diversion  of  such  time  from  his  professional 
practice  is  often  a  serious  menace  to  the  success  of  an  engineer's  business. 

Third.  The  author  feels  that  in  presenting  this  treatise  on  bridge 
economics  to  the  profession,  in  addition  to  his  seven  preceding  books  and 
numerous  technical  memoirs,  he  shall  have  almost  exhausted  all  that  he 
has  to  say  in  print  on  the  subject  of  his  chosen  specialty.  In  other  words, 
his  message  to  the  younger  generation  of  engineers  shall  have  been  deliv- 
ered;  and  he  should  then,  with  a  clear   conscience   about  having  "done 

486 


CONCLUSION  487 

his  bit"  towards  the  development  of  engineering  science,  be  able  to  devote 
his  remaining  working  years  principally  to  serving  the  public  in  an  advisory 
capacity  on  important  engineering  projects — provided  that,  before  the  time 
arrives  for  him  to  pass  on,  the  profession  shall  have  extricated  itself  from 
the  disastrous  slump  into  which  it  was  plunged  in  1914  by  the  advent  of  the 
World  War. 

The  reader  must  not  deduce  from  the  preceding  that  the  author  desires 
to  convey  the  impression  that  his  labors  in  the  field  of  engineering  economics 
are  over — far  from  it! — for  he  has  good  reason  to  expect  that  he  shall  be 
retained  some  day  to  investigate  the  great  economic  problem  of  "Molyb- 
denum Steel  for  Bridges"  in  the  same  manner  in  which  years  ago  he 
investigated  that  of  "Nickel  Steel  for  Bridges." 

The  economic  studies  of  the  last  four  years,  upon  which  this  treatise 
is  mainly  based,  have  been  intensely  interesting;  but  the  work  involved, 
which  (somewhat  unlike  that  of  the  writing  of  the  author's  magnum  opus) 
has  been  chiefly  personal,  and,  in  spite  of  steady  application  and  long  work- 
ing hours,  exceedingly  long-drawn-out,  has  become  rather  overpowering; 
so  that,  it  must  be  confessed,  the  ultimate  completion  of  the  undertaking, 
which  will  not  occur  until  the  book  is  actually  issued,  will  be  decidedly  in 
the  nature  of  a  relief. 

In  another  particular  the  preparation  of  this  treatise  has  differed  from 
that  of  its  predecessor,  which  (as  a  side  issue,  it  is  true,)  necessitated  a 
thorough  search  of  engineering  literature;  because  in  this  case  no  search- 
ing has  been  done,  the  reason  being  that  the  subject  is  ahiiost  entirely  a 
new  one,  and,  consequently,  essentially  independent  of  past  records. 

The  author  hopes  that  this  book  will  prove  of  real  service  to  several 
generations  of  engineers,  notwithstanding  the  fact  that,  on  account  of 
changes  in  practice  due  to  the  rapid  development  of  the  profession,  nearly 
all  engineering  books  are  short-lived.  Such  a  hope  is  not  entirely  without 
foundation,  because  his  little  "De  Pontibus,"  pubhshed  nearly  a  quarter  of 
a  century  ago,  in  spite  of  its  contents  having  been  absorbed  by  its  suc- 
cessor, "Bridge  Engineering,"  had  a  steady  sale  until  about  the  end  of 
1920,  when  the  publishers  let  it  go  out  of  print  because  of  its  low  price 
combined  with  the  exceedingly  high  cost  of  paper,  press-work,  and 
binding. 

In  conclusion,  there  is  a  suggestion  which  the  author  would  like  to  make 
concerning  a  possible  utility  for  this  work  in  combination  with  its  immediate 
predecessor;  but  he  has  long  debated  as  to  the  advisability  of  offering  it, 
fearing  that  some  of  his  readers  may  either  misconstrue  his  motive  or 
charge  him  with  undue  conceit  concerning  the  value  of  his  technical  pro- 
ductions. However,  he  has  decided  to  run  the  risk;  because  he  greatly 
desires  that  the  results  of  the  long  and  arduous  labor  which  he  has  put 
upon  their  preparation  shall  be  utilized  to  the  utmost  for  the  benefit  of  all 
future  young  engineers  who  have  the  ambition  to  specialize  in  bridgework. 
The  suggestion  is  this:  " 


488  ECONOMICS    OF   BRIDGEWORK  Chapter  XLV 

If  a  young  engineer  of  fine  intelligence,  great  energj^ ,  unceasing  persevre- 
ance,  and  high  ambition,  who  has  had  during  his  technical-school  course  a 
thorough  training  in  the  theoretical  portion  of  bridge  designing  and  has 
systematically  continued  to  read  and  study  concerning  bridgework  during 
a  practice  of  five  or  six  years,  devoted  mainly  to  the  various  ramifications 
of  that  specialty  in  computation  room,  drafting  office,  manufacturing  shops, 
and  field,  wishes  to  become  a  bridge  expert  and  carry  on  an  independent 
consulting  practice,  he  can  do  so  by  adopting  the  following  procedure: 
Let  him  devote  all  of  his  time  for  an  entire  year  to  the  reading  and  re-read- 
ing of  "Bridge  Engineering"  and  "Economics  of  Bridgework"  and  to  solv- 
ing, by  the  use  of  these  books,  numerous  examples  of  all  kinds  upon  assumed 
data,  so  as  to  obtain  actual  experience  in  the  computation  of  secondary 
stresses  and  deflections,  in  the  designing  of  the  various  types  of  bridges,  in 
the  determination  of  economic  layouts  for  all  kinds  of  assumed  conditions, 
in  the  expeditious  making  of  cost  estimates,  in  the  writing  of  specifications 
for  manufacture  and  erection  of  substructure,  superstructure,  and  ap- 
proaches, and  in  the  drafting  of  sound  engineering  contracts.  Such  work 
could  best  be  done  as  a  post-graduate  course  in  one  of  the  leading  technical 
schools;  but  this  is  not  really  essential,  because  such  a  young  man  as  the 
one  described  should  certainly  be  able  to  carry  on  his  studies  unaided. 
Again,  it  could  be  carried  out  well,  by  taking  longer  time,  were  the  young 
man  in  the  employ  of  a  consulting  engineer,  a  bridge  manufacturing  com- 
pany, or  a  bridge  erector.  The  author  feels  confident  that,  upon  the  com- 
pletion of  the  training  above  recommended,  the  young  man  under  con- 
sideration would  be  truly  entitled  to  term  himself  a  Consulting  Bridge 
Engineer,  and  his  success  in  that  capacity  would  practically  be  assured. 


APPENDIX 


The  following  is  a  chronologically  arranged  list  of  the  author's  various 
investigations  and  writings  on  the  subject  of  bridge  economics,  extending 
over  a  period  of  thirty-seven  years: 

In  1883,  a  paper  on  ''Economy  in  Struts  and  Ties." 

In  1884,  a  chapter  on  "Economy"  in  " The  Designing  of  Ordinary  Iron 
Highway  Bridges." 

In  1891,  a  paper  in  "Indian  Engineering"  on  "Economic  Span- 
Lengths." 

In  1897,  a  chapter  on  "True  Economy  in  Design"  in  "De  Pontibus." 

In  1897,  an  elaborate  investigation  of  the  economics  of  cantilever 
bridges,  published  in  the  last-mentioned  work. 

In  1906,  a  complete  investigation  of  the  economics  of  steel  trestles, 
which  was  later  incorporated  in  "Bridge  Engineering." 

In  1907,  an  extensive  paper  on  "Nickel  Steel  for  Bridges,"  published  by 
the  American  Society  of  Civil  Engineers  and  awarded  its  Norman  Medal. 

In  1909,  a  paper  written  in  French  for  Le  Genie  Civil  and  entitled 
"  Une  Etude  Economique  de  VEmploi  de  I'Acier  au  Carbone  a  Grande  Resist- 
ance pour  la  Construction  des  Fonts." 

In  1913,  a  paper  on  "The  Possibilities  in  Bridge  Construction  by  the 
Use  of  High-Alloy  Steels,"  published  by  the  American  Society  of  Civil 
Engineers,  and  awarded  its  Norman  Medal. 

In  1914,  a  paper  on  "Alloy  Steels  for  Bridgework,"  presented  to  the 
International  Engineering  Congress  of  the  San  Francisco  World's  Fair. 

In  1916,  a  chapter  on  "True  Economy  in  Design,"  in  "Bridge  Engineer- 
ing," being  an  expansion  of  a  similar  chapter  in  "De  Pontibus." 

In  1917,  a  series  of  three  lectures  on  "Engineering  Economics,"  deliv- 
ered to  the  Engineering  Alumni  Association  of  the  University  of  Kansas. 

In  1917,  a  paper  on  "The  Economics  of  Steel  Arch  Bridges,"  presented 
to  the  American  Society  of  Civil  Engineers,  published  in  its  "  Proceedings," 
and  awarded  its  Norman  Medal. 

In  1918,  a  paper  entitled  "Comparative  Economics  of  Cantilever  and 
Suspension  Bridges,"  presented  to  the  Western  Society  of  Engineers  and 
published  in  its  "Proceedings." 

In  1919,  a  paper  on  "Economic  Span-Lengths  for  Simple  Truss  Bridges 
on  Various  Types  of  Foundation,"  presented  to  the  last-mentioned  society 
and  published  in  its  "Proceedings." 

489 


490  APPENDIX 

In  1919,  a  paper  entitled  "Possibilities  and  Economics  of  the  Trans- 
bordeur/'  presented  to  the  Institution  of  Civil  Engineers  of  Great  Britain, 
and  published  as  the  basis  of  two  editorials  in  Le  Genie  Civil. 

In  1920,  a  joint  paper  with  Mr.  H.  Malcolm  Priest  on  "Comparative 
Economics  of  Continuous  and  Non-Continuous  Trusses,"  presented  to  the 
Engineers'  Society  of  Western  Pennsylvania  and  published  in  its  "Pro- 
ceedings," 

In  1920,  a  paper  for  the  same  society  on  "Comparative  Economics  of 
Wire  Cables  and  High-Alloy-Steel  Eyebar-Cables  for  Long-Span  Suspen- 
sion-Bridges," and  pubhshed  in  its  "Proceedings." 

In  1920,  a  rnemoir  entitled  "De  VEynyloi  Econoviigue  cles  AlUages 
d'Acier  dans  la  Construction  des  Fonts,"  published  in  condensed  form  by  the 
Academic  des  Sciences  on  July  12,  1920,  and  in  full  by  Le  Genie  Civil  on 
July  24,  1920. 

In  1920,  a  paper  entitled  "Bridge  versus  Tunnel  for  the  Proposed  Hud- 
son River  Crossing  at  New  York  City,"  presented  to  the  American  Society 
of  Civil  Engineers  and  published  in  its  "Proceedings." 

In  1920,  an  as-yet-unpublished  paper  on  "Economics  of  Reinforced- 
Concrete,  Steam-Railway  Bridges." 

In  1920,  a  paper  on  "Economics  of  Movable  Spans,"  presented  to  the 
American  Railway  Engineering  Association,  but  not  yet  published. 


INDEX 


Abrams,  Prof.  Duff  A.,  395 
Abrasion  of  bridge  paint,  445 
Abutments  for  arches  with  filling,  226 
Abutments    with    wing-walls     versus    buried 

piers,  114 
Academic  des  Sciences,  26 
Accessibility  to  paint  brush,  201 
Accidents  in  shops,  370,  371 
Accumulators,  312 

Accuracy  in  calculations,  limits  of,  359 
Additions  to  future  loadings,  16 
Advantages    of    ideal    method    of    contract- 
letting,  352-354 
Aerial  ferry,  318 
Aesthetics,  123 

pier-shafts,  168 
Age  of  cement,  393,  394 
Aggregate  for  concrete, 

light,  198 

prices  of,  23 

reduction  of  voids  in,  389 

volume  of  voids  in,  386 
Agreeableness     of     traversing     bridges     and 

tunnels,  54,  56 
Air-spraying  of  paint,  422 
Algiers,  319 

Alignment  and  grade,  119 
Alligatoring  of  paint,  434 
Allowance  for  clearance,  214 
Allowance  for  expansion,  215 
Alloy  steels, 

carbon  steel,  comparison  with,  32,  33 

criterion  for  plate-girders  of,  27 

economic  comparisons  of,  44—51 

economics  of,  26-52 

prices  of,  44 

tests  of,  38-43 

use  in  bridgework,  33 
Alternating  versus  direct  current,  312 
Alternative  methods  of  erection,  399 
Aluminum  steel,  33,  34 

Analysis  of  details  and  joints  sometimes  im- 
practicable, 201 
Anchor  arms,  economic  lengths  of,  100,  258 
Anchor  piers  for  cantilever  bridges,  compu- 
tations of,  94 
Anchor  span,  economic  length  of,  259 

491 


Anchorages  for  suspension  bridges,  94,  267 
Anchored  ends  versus  free  ends  for  stiffening 

trusses,  268 
Angles,  single,  in  tension,  204 
Annual  costs,  total,  contrasting  of,  14 
Annual  expenses,  14 

Anticipating  accidents  in  shop,  370,  371 
Anticipating  the  future,  16 
Anticipating  troubles,  371 
Antoine,  Marc,  35 
Appearance  of  reinforced    concrete    bridges, 

456 
Appendix,  489 
Application  of  paint,  422 

after  cleaning,  446 
Approaches, 

bridges   and    tunnels,    time   expended   in 

climbing  up  and  down,  56 
economics  of,  113 
nature  of,  483 
spiral,  59 

suspension  bridges,  266 
timber  trestle,  21 
Arbitrary  power  of  resident  engineer,  382 
Arches, 

combination  of  stresses  in,  135 

Fraser  River  Bridge  at    Lytton,    B.   C, 

246 
reinforced-concrete,  225-230 
abutment,  226 
erection  of,  406 
inequality  in  length  of,  227 
ribs,  types  of,  227 
rise  of,  226 

steel  bottom  chords,  229 
steel, 

cantilever,  238 

economics  of,  232-249 

erection  of,  402 

formulae  for  weights  of  metal  in,  239, 

240,  248 
limiting  span-length  for,  241 
pile  foundations  for,  244 
tabulation  of  salient  features  of,  234 
weights  of,  compared  to  trusses,  238, 
239 
Waikato  River  Bridge  at  Cambridge,  N. 
Z.,  247 


492 


INDEX 


Arches, 

Waikato  River  Bridge  at  Hamilton,  N.  Z., 
246 
Arnold,  Col.  Bion  J.,  8 
Arrangement  of  deck,  128 
Arrangement  of  riveting,  199 
Arroyo  Seco  Bridge  at  Pasadena,  Calif.,  248 
Asphalt,  Ufe  of,  452 
Asphalt  pavements,  188 
Assembling,  376 
Assembling  in  shops,  378,  379 
Assistant  Engineer  of  Construction,  383 
Auditor,  384 
Austin,  Texas,  bridge  over  Colorado  River, 

248,  249 
Author's  report  to  S.  P.  E.  E.,  3 
Automatic  brakes  on  Uft  bridges,  295 
Automobile  travel  in  tunnels,  53 
Auto-truck  loadings,  125 
Availability  of  supplies,  123 
Avoidance  of  special  material,  205 

B 

Backstays,  94 

suspending  floor  from,  266 
Balance-beam    bascule    bridge.    Brown,    for 

Mystic  River,  297,  308 
Balanced-cantilever  type  of  girder,  222 
Balancing  chains  in  lift  bridges,  294 
Ballasted  decks,  182,  183,  185,  186 

Ballast    resting    directly    on    steel    plate, 
183 

Ballast     resting     on     reinforced-concrete 
slab,  183 
Banks,  nature  of,  483 
"Bare  necessities  only,"  principle  of,  461 
Bascules, 

Brown  balance-beam,  298 

economics  of,  289 

heel-counterbalanced-trunnion  type,  290 

heel-trunnion,  297 

Housatonic  River  Bridge,  298,  308,  309 

Mystic  River  Bridge,  298 

quantities  for,  299 

singlo-lcaf  versus  double-leaf,  289 

swing-span,  comparison  with,  284,  285 

vertical-lift,    comparison    with    285-287, 
302 

wind  pressure  on,  316 
Base  for  pavement  on  lift  bridges,  295  ' 
Bases    of    pedestals,    plain    concrete    versus 

reinforced,  173 
Batten  plates,  200,  203 
Beach,  Major  General  Lansing  H.,  459 
Beams,  intensities  for  compression  flanges  of, 

137 
Mending  of  long  pieces  undosiral  )1(\  '_'  I  I 
J{(!Hsotii('r   process,  modification   of,  for  high 

grade  steel,  35 
Beveled  cuts,  206,  212 


Bitulithic  pavements,  188 

Bituminous   concrete   floors,    unsatisfactory, 

427 
Bituminous  pavements,  188 
Blacksmith  shop,  378 
Blank  forms,  360 
Blockade  of  tunnel  traffic,  56 
Block  pavements,  426 
"Bloom,"  456 

Bob-taUed  swing  versus  ordinary  swing,  288 
Boca  del  Rio  Bridge  painting,  439 
Boiled  linseed  oU,  435 
Bond,  Colonel  P.  S.,  460 

Bonus,  method    of    division    of    among    em- 
ployees,   348 
Boring,  377 
Bottom,  nature  of,  483 

Box  sections  for  compression  members,  261 
Braced  towers  versus  solitary  columns,  254 
Braked  trains,  thrust  of,   140 
Brake  power  for  bascules,  316 
Brake  resistance,  315 
Brakes,  automatic,  on  lift  bridges,  295 
Brazil,  paint  for,  440 
Breakdown  of  machinery,  315 

vehicles  in  tunnels,  57 
Bridges, 

agreeableness  of  crossing,  54,  56 
approaches, 

data  concerning,  in  "Bridge  Engineer- 
ing," 114 
economics  of,  113 
arch,  steel,  economics  of,  232-249 
combined,  129,  131 
comparative  economy  of,  14 
contractors,  general  fieldwork  of,  383 
economics,   list   of  author's  writings  on, 

489,  490 
entrances  and  exits,  separation  of,  55 
height  of  climb  over,  54 
manufacturers'  standards,  205 
movable,  284-309 

cost  of  operation  of,  55 
operated  by  combustion  engine,  311 
operated  by  electricity,  311 
operation    by    hydraulic    pressure    or 

compressed  air,  311 
power  for  operating,  cost  of,  55 
projects,  promotion  of,  20 
reinforced-concrete,  218-231 

comparison  with  steel  bridges,  64-66 
small  cost  of  maintenance  and  repairs 
for,  64 
replacing  of,  403,  404 
riveted  versus  pin-conno<'te<l,  72 
sanitation  on,  56 
siniple-truss,    economic    limit    of    length 

for,  84 
spiral  approaches  to,  59 
steel,  67-71 


INDEX 


493 


Bridges, 

comparison    with    rciiiforced-ooncrete 

bridges,  64-66 
life  of,  64 
strengthening  old,  409,  416,  417 
tunnels,  comparison  with,  53-60 
author's  paper  on,  55 
comparative  economics  of,  12,  53 
cost  curves  for,  57 
costs  compared,  54 
unit  prices  for,  57 
Brine  drippings  from  refrigerator  cars,  415, 
453 
protection  against,  443 
Urooklyn  Bridge,  266 
Brooklyn  Engineers'  Club,  457 
Brown,  Thomas  Ellis,  310. 

balance-beam  bascule,  291,  297 

bridge  over  Mystic  River,  298,  308 
Brown,  Thomas  ElHs,  Jr.,  290 
Brush  for  painting,  character  of,  448 
Buckle-plate,  stiffened,  195 
Buffers  for  lift  bridges,  295 
Buildings  and  plant,  384 
Built  piles,  296 

Buried   piers   versus   abutments   with   wing- 
walls,  114 
Burlap  for  water-proofing,  183 
Burrard  Inlet  proposed  bridge  at  Vancouver, 

B.  C,  131 
Byrne,  Edward  A.,  195,  264 


Cables, 

advantages  and  disadvantages  of  various 

types  of,  268,  269 
formulEe  for  weights  of,  272-275 
suspension  bridge,  economic  rise  of,  265, 

266 
vertical-lift  bridges,  295 
Caissons, 

building  up  of,  382 

comparison  with  cribs  filled  with  piling, 

173 
reinforced-concrete,  169 
side  friction  on,  156 
Calcutta    bridge    over    Hoogly    River,    pro- 
posed, 296 
Cambering  plate-girders,  207 
Cambridge    arch    bridge    over    the    Waikato 

River,  247 
Camden  and  Philadelphia,   proposed   trans- 

bordeur  for,  335 
Camps,  385 

Canady,  C.  M.,  208,  365 
Cantilevers, 
aesthetics,  83 

alloy  steels,  criterion  for,  27,  29 
anchor  piers,  94 
arches.  238 


Cantilevers, 

combination  of  stresses,  135 
economic  lengths,  94 

of  anchor  arms,  100-102 
economic  span-lengths,  258 
economics  of,  257-262 
erection,  399,  401 
illegitimate  use,  83 
inclined  struts  over  main  piers,  260 
intermediate  trusses,  260 
legitimate  economies  in,  259,  260 
limiting  widths  of  structure,  94 
Hve  loads,  127 
minimum  width,  84,  85 
new  type  of,  economics  involved,  87-89 
pedestals,  260 
piers,  94 
rigidity,  83 

riveted  versus  pin-connected  types,  261 
simple-truss    bridges,    comparison    with, 

83-89 
solitary  piers,  pedestals  for,  260 
splaying  of  trusses,  260 
standard  types,  84,  85 
suspension  bridge,  comparative  economics 
of,  90-112 
economics  as  affected  by  use  of  alloy 

steels,  110 
highway  bridges,  106 
resume  of  investigation  of,  108,  109 
truss  depths,  259 
types  of,  257-262 
A,  86 

C,  economics  of,  84,  85 
vertical-lift  combination,  295 
vibration  in,  83 
weights  of  metal  in,  31 
Cantilevered   versus   counterforted   retaining 

walls,  231 
Capital  Account,  409 
Capital  and  Labor,  338 
Capitalization  of  operation  and  maintenance, 

15 
Carbon-molybdenum  steel,  37 
Carbon-monoxide,  cumulative  action,  53,  56 

in  tunnels,  53 
Carbon  steel,  45 

alloy  steel  comparison,  32,  33 
Carmol  steel  comparison,  44 
Card  indices,  360 
Carmol  steel,  37,  45 

carbon  steel  comparison,  44 
tests  of,  42 
Carrothers,  D.  D.,  438 
"Carrying  Bridges  Over,"  409 
Carrying  structure,  314 
Cartlidge,  C.  H.,  288 

Castings  at  column  feet  unnecessary,  204 
Cast  iron  in  bridges,  204 
Causes  of  paint  deterioration,  444 


494 


INDEX 


Cement, 

age  of,  393,  394 

concrete  floors,  unsatisfactory,  427 

paints,  437 

prices,  23 

protection  of,  382 

testing,  380 
Center-bearing     versus     rim-bearing     swing- 
spans,  287 
Centrifugal  force  for  old  bridges,  412 
Chains,  balancing,  for  lift  bridges,  294 
Chalfant,  J.  G.,  407,  424 
Chamfering,  375 
Changes  on  drawings,  359 
Channel  flanges  turned  in,  203 
Channels,  shifting,  122,  293 
Charts  of  progress,  381 
Chattahoochee  River  crossing  at  West  Point, 

Ga.,  471 
Checking  computations,  359 
Checking  of  materials,  380 
Cheesman  &  Elliot,  432 
Chess  (floor  of  ponton  bridge),  470 
Chrome-molybdenum-steel  cables,  282 
Chrome-nickel  steel,  37 
Chrome  steel,  46 

Chromol  steel  comparison,  45 

tests  of,  38 
Chrome-vanadium  steel,  37 
Chromium-molybdenum  steel,  37 

best  composition  of,  51 
Chromium-vanadium-molybdenum  steel,  37 
Chromol  steel,  37,  46 

best  composition  of,  51 

cables,  282 

chrome  steel  comparison,  45 

Chrovanmol  steel  comparison,  51 

Nicmol  steel  comparison,  51 

tests  of,  38 

(treated),  43 
(untreated),  43 
Chrovanmol  steel,  37,  49 

Chromol  steel  comparison,  51 

Chrovan  stCel  comparison,  48 

tests  of,  40 
Chrovan  steel,  37,  49 

Chrovanmol  steel  comparison,  48 

tests  of,  40 
City  of  New  Orleans,  319 
Clarke,  Ernest  Wilder,  337 
Clarke,  Major  Leon  L.,  310 
Classes  of  military  bridges,  463 
Classification, 

bridges,  410 

loadings,  412 

low,  for  old  bridges,  414 

Train  TjoadJTigs,  413 
Cleaning, 

application  of  paint  after,  446 

metalwork,  245,  422 


Cleaning, 

for  shop  coat,  441 
Clearance  allowance,  214 
Clearances, 

above  high  water,  122 

ample,  216,  316,  317 

between  bottom  of  shaft  and  cofferdam, 

171 
criterion  for  economics  of  bascules  and 

vertical  lifts,  309 
necessity  for,  214,  215 
Clear  waterway,  122 
CUmatic  influences  on  paints,  438 
Climax  Molybdenum  Company,  36 
Climb  over  a  bridge,  height  of,  54 
Clutches,  313 

Cocked-hat  in  pier  shafts,  169 
Cofferdams, 

open-dredging  comparison,  171 
sealing  of,  172 
Collection  of  data,  359 
Colorado  River  Bridge  at  Austin,  Texas,  248, 

249 
Colors  of  paints,  428 
Columns, 

best  number  of  per  bent,  224 

castings  unnecessary  for  feet,  204 

formulce,  139 

reinforced-concrete,  223 

sections,  best,  255 

spacing,  economic,  253 

steel  trestles,  method  of  proportioning  of, 

134 
tests.  Report  of  Committee  on,  136,  137 
Combination  of  stresses,  133 

stresses  in  cantilever  bridges  and  arches, 
135 
Combination  of  vertical  lift  and  cantilevers, 

295 
Combined  bridges,  129,  131 
grouping  of,  129,  130 
live  loads  for,  132 
Coniljustion    engine    for    oiiorating    bridges, 

311 
Commercial  influences,  120 
Comparative  economics, 
bridges  and  tunnels,  53 
Cantilever  and  Suspension  Bridges,  268 
difTcrcnt  types  of  ordinary  steel  bridges, 

07 
formula  for,  14 

of    Wire-Cables    and     High-Alloy    Steel 
Eye-bar-Cables   for   Long   Span 
Suspension-Bridges,  263,  267 
steel  and  reinforced-concrete  bridges,  65 
Compensating  fac^tors  in  economic  compari- 
sons, 16 
Compensation  for  inspection,  3()1 
ConipolKion    eliminated    l)y    (X)st-phis    con- 
tracts, 342 


INDEX 


495 


Competition  for  students  on  cost  estimating, 

141 
Compressed  air  for  bridge  operation,  311 
Compression  flanges  of  beams,  intensities  for, 

137 
Compression  members, 

box  sections  for,  261 

economic  sections  of,  199 
Computations,  checking  of,  359 
Computing,  short  cuts  in,  92 
Concluding  suggestion  by  author,  487,  4(S8 
Conclusion,  486 
Concrete  (see  also  Reinforced  Concrete) 

aggregate,  prices  of,  23 
volume  of  voids  in,  386 

amount  of  water  for  mixing,  392 

arch-spans,  erection  of,  406 

best  proportion  of  materials  for,  387-389 

bridges,   water-proofing   of,   451 

cracks  in,  455 

depositing  under  water,  382 

encasement,  442 

fluidity  of  mixture,  391 

forms,  steel  versus  timber  for,  170 

girder  bridges,  erection  of,  406 

jigging  of  freshly-made,  392,  393 

leaching  of  by  percolation  of  water,  454 

light  aggregate  for,  198 

manufacture,  economic  problems  in,  387 

military  bridges,  476 

mixing,  economics  of,  386-395 
manner  and  time  of,  391 

one-man  stones  in,  386 

pavements,  188 

payment  for,  386 

pier- shafts,  reinforcing  of,  167 

plain  versus  reinforced,  for  pedestal  bases, 
173 

protection  of,  394 

stone  masonry  for  piers,  comparison,  167 

stones,  large,  use  of,  392 

timber  decks  for  highway  bridges,  com- 
parison, 187 

working  stresses  for,  219 
Condemnation  of  old  bridges,  ruling  for,  407 
Conditions  affecting  layouts  of  bridges,  116 
Congestion  of  traffic  at  entrance  and  exit,  54 
Connections,  entering,  216 
Conscientious  contractors,  342 
Conscientious  workmen,  342 
Construction,  Engineer  of,  383 
Construction  facilities,  123 
Continuity  of  trusses,   summary  of  conclu- 
sions from  investigation,  81 
Continuous  trusses 

divided-triangular  trusses,  78,  80 

economics  affected  by  semi-cantilevering, 
81 

effect  of  reversing  stresses  on,  77 

highway  bridges,  78 


j     Continuous  trusses, 

legitimate  use  of,  75 

non-continuous  trusses,    comparison,  75- 
82 

Petit  trusses  for,  78,  81 
Continuous  versus  simple  reinforced-concrete 

girders,  221,  222 
Contract-letting,  economics  in,  337-357 

ideal  system  of,  343,  344 
advantages  of,  352-354 
objections  raised  to,  354—356 

importance  of,  337 

unit  prices,  340 

various  methods  of,  339 
Contractor, 

economic  subjects  for  study,  383 

salary    on    cost-plus    jobs    objectionable, 
348,  349 
Contracts,  expediting  finishing  of,  173 
Conveyance  of  power,  312 
Copying  surveys  from  field  books,  381 
Corners,  round,  in  plate-girders,  207 
Corrective  ratio,  346,  347 
Corrosion,  415 

prevention  of,  421 
Corthell,  Dr.  Elmer  L.,  12 
Cost, 

bridges  and  tunnels,  57,  58 

estimates  for  bridges,  economics  in,   141 

estimating,  examples  of,  142-145 

first,  16 

movable  spans,  297 

operation,  55 

problems     for     solution      by     students, 
146-149 

records,  360 

shopwork  on  pins  and  holes,  73 

total  annual,  contrasting  of,  14 
Cost-plus  method,  objections  to,  343 

author's  experience  with,  343 

eliminates  competition,  342 
Cotton    drilling     for    water-proofing    decks, 

183 
Council  Bluffs  Bridge,  21 
Counterforted  versus  cantilevered  walls,  231 
Counters,  over-stress  of,  423 
Counterweights,  materials  for,  294 
Covell,  V.  R.,  407,  424 
Covering  power  of  paint,  436 
Cover-plates  for  top  flanges,  200 
Cracks  in  concrete,  455 
Cranes,  366,  376,  381 
Creosoting,  188 
Crescent  trusses,  272 
Cribs  and  caissons,  building  up  of,  382 
Cribs  for  foundations,  173 

military  bridging,  469 
Criterion, 

clearance  for  bascules  and  vertical  lifts, 
309 


496 


INDEX 


Criterion, 

economics  of  primary  truss  members,  26 

military  bridge  criterion  is  victory,  462 
Crooked  stringers,  466 
Cross  girders,  spacing  of,  192 
Cross-section  of  deck,  128 
Crown-hinge,  location  of,  235 
Crowning  of  roadway,  426 
Crystallization  of  metal,  416 
Curbs,  189 
Current,  swiftness  of,  483 

reversal,  122 
Curving  ends  of  girders,  211 
Cut-stone  masonry  versus  concrete  for  piers, 

167 
Cutting  metal,  374 
Cylinder  piers,  168 

repairs  to,  421 

D 

Damages,  382 

failure  to  water-proof,  453 
faulty  inspection,  362 
Danger  from  fire,  113 
Data, 

collection  of,  359 

concerning  bridge  approaches  in  "Bridge 
Engineering,  "114 
Davies,  J.  Vipond,  8 
Decisions  by  resident  engineer,  381 
Decks, 

arrangement  of,  to  accommodate  several 

lines  of  traffic,  128 
ballasted,  182,  183,  185,  186 
drainage  of,  183 
economics  of,  182-198 
highway  bridges,  187 

concrete  versus  timber  for,  187 
military  bridges,  474 
open  timber,  182,  184 
open-web,    riveted    spans,   economics   of, 

70 
plate-girder  spans,  economics  of,  6S 
timber,  195 

weight  reduced  to  mininnmi,  194 
width  of,  127 
DefensibiHty  of  military  bridges,  484 
Definition  of  economics,  6 
Delaware  River  bridge  between  l'hil:uloli)lii:i 

and  Camden,  proposed,  318 
Depositing  concrete  under  water,  382 
Depths, 

descent  into  a  tunnel,  54 
economic,  of  trusses,  176 
floor  beams,  economic,  185 
foundations,  122 
girders  in  viad\icts,  203 
pier  shafts  below  water,  170 
plate-girders,  er^onomic,  with  rivct-etl  end 
coiHiections,   179,   180 


Depths,  -^ 

stringers,  economic,  185 
water,  483 
Derrick  cars,  398 

Descent  into  a  tunnel,  depth  of,  54 
Design, 

details,  203 
economics  of,  199-201 
shop  considerations,  366 
Destruction  due  to  neglect  of  water-proofing, 

457 
Detailing,  economics  of,  199-201 

vertical  lifts,  economics  in,  294 
Details,  designing  of,  203 
skimping  of,  133,  201 
Deterioration, 

paint,  causes  of,  444 
steel  structures  due  to  wear,  423 
Determination, 

economic  span-lengths,  158 
layouts,  116-124 
time  for  repainting,  445 
Detroit  River  proposed    bridge,    estimating 

cost  for.  111,  146 
Detroit  Superior  Graphite  paint,  438,  439 
Development  of  true  economy,  2 
Diagrams,  18 

Direct  current  versus  alternating,  312 
Discharging  employees,  381 
Disruptive  force  of  freezing  water,  455 
Distance  from  springing  to  bottom  of  base, 

226 
Diversion  of  traffic  during  replacement,  405 
Divided-triangular    trusses    for    continuous 

spans,  78,  SO 
Division  of  bonus  among  employees,  348 
Dogs,  476 

Double-leaf  versus  single-leaf  bascule,  289 
Double  tracking,  future,  21 
Double-track  railway  trestles,  252 
Doubling  of  trusses,  future,  21 
Doubling-up  of  old  bridges,  407 
Drainage, 
deck,  183 
roads,  454 
Drawings, 

changes,  359 
luichecked,  359 
Drawing  temperature,  best,  44 
Driers,  use  of,  435 
Drift  bolts  in  military  bridges,  477 
Drift,  prote(!tion  against,  485 
Drifting  ice,  122 
Drilling    (cotton)    for   water-proofing  decks, 

183 
Drilling  from  soliil,  208,  375 
Drills,  portable,  379 
Drippings  from  Inine,  415 
Dulutli  proi)()sed  lift  bridge,  310 
"Duiiih  licll"  pier-shafts,  168 


INDEX 


497 


Duplication,  209 

Dutch  Boy  Rod  Lead,  432 

E 

Earle,  Thomas,  365,  372 

Earth-thrust,  influence  of,  228 

East  Omaha  Bridge  over  the  Missouri  River, 

21,  131,  168 
East  River  Bridge,  266 
Economic, 
factors,  8 

limits,  wide  range  of,  16 
investigation     of     engineering     practice, 

principle  of,  6 
problem,  8 
span  lengths     for     simple-truss     bridges, 

150-165 
resume  of  results  for,  161-164 
Economics, 

definition  of,  6 
engineering,  a  treatise  on,  3 
principles,  general,  6 
studies,  necessity  for,  7 
study  of,  in  technical  schools,  3 
versus  expediency,  15 
Economy, 

comparative,  formula  for,  14 
true,  development  of,  2 
Effect  of  wind  pressure  on  moving  spans,  293 
Efficiency, 

American,  2 
national,  increasing,  2 
power,  definition  of,  311 
transbordeur,  330 
Elasticity  requisite^  for  water-proofing   ma- 
terial, 452 
Electric, 

lamps  in  shops,  367 
railway  bridges,  187 
loading,  126 
tracks,  190 
Electricity   as  power  for  operating  bridges, 

311,  312 
Electrified  steam  railroads,  126 
Electrolytic  action,  455 
Electro-metallurgical  process,  33 
Elevated  railroads,  250-256 

economic  span-lengths  for,  254 
economics  of,  250-256 
pin-connected,  73 
Elimination  of  noise  of  gearing,  313 
Elimination    of   unnecessary   transportation, 

366 
Embankments,  113,  115 
Embedded  steel,  necessity  for  water-proofing 

455 
Employees, 

character  of,  385 
discharging  of,  381 
force  of,  383 


Employees, 

keeping  busy,  380 
percentage  of  profit,  348 
Encased  steel,  necessity  for  water-proofing, 

455 
Encasement,  186 
concrete,  442 
floor,  193 
End  floor  beams,  omission  of,  203 
Engine,  gasoline,  multi-cylinder,  313 
Engineer, 

aid  contractor,  381 
Construction,  383 
importance  of  his  work,  3 
long  working  hours  for  field,  380 
resident,  instructions  to,  380 
War  work,  459 
Engineering, 

economics,  importance  of  study  of,  3 
lectures  to  University  of  Kansas,  4 
treatise  on,  3 
fieldwork,  380 

office  work,  economics  of,  358-360 
Enlargement,  future,  121 
Entering  connections,  214,  216 
Enterprise,  economics  of  proposed,  7 

paying,  8 
Entrances  to  bridges  and  tunnels,  separation 

of,  55 
Equipment  for  repairs  and  renewals,  420 

tools,  374 
Erection, 

alternative  methods  of,  399 
arch  spans,  402 
cantilevering,  399 
cantilevers,  401 
concrete  arch-spans,  406 
concrete-girder  bridges,  406 
considerations,  123 

design  for,  214-217 
eccentric  falsework,  399 
economics  of,  396-406 
elevation  from  ground,  400 
floor-system  in  advance  of  trusses,  215, 

216 
flotation,  400 
girder  spans,  397 
long  spans,  400 
medium  spans,  399 
methods,  123 
plant,  402,  403 
protrusion  method  of,  399 
specialization  of,  396 

standard  plant   and  equipment  for,  397, 
starting  at  center  panel,  215 
steel  bridges,  397 
suspended  platform,  400 
suspension  bridges,  401 
temporary  suspension  spans,  400 
viaducts,  398 


498 


INDEX 


Estimates; 

costs  for  bridges,  economics  in,  141 

monthly,  to  be  made  promptly,  381 
Estimating,  examples  of,  142-145 
Examples, 

cost  estimating,  142-145 

use  of  economic  curves  for  movable  spans, 
304-308 
Excessive  live  loads,  125 

Excrescence  of  magnesia  and  other  salts,  456 
Existing  bridges,  utilization  of,  480 
Exits  from  bridges  and  tunnels,   separation 

of,  55 
Expansion  allowance,  215 

joints  in  pavements,  219 
Expediency  versus  economics,  15 
Expediting  finishing  contracts,  173 
Expenses,  annual,  14 
Expert  opinion,  gratis,  7 
Explosives,  storage  of,  382 
Extra  metal  required  to  support  one  excess 
pound  of  extraneous  load,   197, 
198 
Extras,  381 

Extra  work,  not  a  punishment,  1 
Eye-bar-cable  suspension-bridges,  277 

quantities  of  various  materials  in,  278 


Fabrication,  designing  of  shops  to  suit,  366 

Facilities  for  construction,    123 

Factors, 

affecting  layouts  of  bridges,  116 

affecting  results  in  painting,  446 

compensating,  17 

economic,  8,  17 

safety,  small  for  military  bridges,  462 
P^ailure  to  water-proof,  damage  from,  453 
Falsework, 

fitness,  382 

washout,  15 
Fatigue  of  bridge-metal  a  myth,  416 
Features,  general,  of  structure,  120 
Field, 

coats,  application  of,  434 

engineers,  long  working  hours  for,  380 

inspection,  364 

organization,  383 

property  of  the  engineers,  381 
Fieldwork, 

economics  of  l)ridgc  engineering,  380 

general,  of  bridge  contractors,  383 

layout  for,  380 

time  schedule  of,  380 
Filing,  359 
Fire,  danger  from,  1  13 

protcf^tion  for  timber  bridges,  420 
Fire-proof  paints,  420 
First  cost,  16 
Fish,  Prof.  J.  C.  L.,  6 


Fitness  of  falsework  and  forms,  382 
Fixed-span  bridges,  ratios  of  cost  for,  with 
various    clearances    above    high 
water,  331 
Flanges  of  beams,  intensity  of  compression 

for,  137 
Flanking  spans,  293 
Flashing,  183 
Flat  scale  of  wages,  370 
Floating  bridges,  470 
Floods,  122 

protection  against,  485 
Floor  beams, 

economic  depths  of,  185 
sections,  186 
Flooring  in  military  bridges,  474 
Floor  records,  427 
Floor-systems, 

economic  depths  of,  for  truss  bridges,  177, 

178 
economics  of,  182-198 
highway  bridges,  190-200 
railway  bridges,  184 
stringerless  type  of,  193,  194 
Floors, 

maintenance  of,  425 
shops,  374 
Flotation  method  of  erection,  400 
Fluidity  of  mixture  of  concrete,   increasing, 

391 
Foot  bridges,  military,  473 
Footings,  223 
Footwalks,  21 

widths  of,  128 
Force  of  employees,  385 
shops,  size  of,  380 
workmen,  373 
Foresight,  16 
Foreword    by    Major    General    Lansing    H. 

Beach,  459 
Forge  work  to  be  minimized,  211 
Forms, 

blank,  360 

concrete,  steel  versus  timber  for,  170 
fitness  of,  382 
FormultE 

comparative  economy,  14 
weights  of  metal  in  arches,  239,  240 
weights  of  suspension  bridges,  272-275 
approximate  accuracy  of,  248 
Fort  Leavenworth  bridge  over  the  Missouri 

River,  repairs  to,  408 
Foundation  considerations,  122 
arches  on  i)iling,  244 
deep,  122 

e(;onomi<Ts  of,  167-174 
loadings  on  deep,  156 
piles,  ignoring  of  imi>act  on,  140 
Foundry,  378 
Four-angle  columns,  212 


INDEX 


499 


l'"our-column    versus    two-column    structures 

for  elevated  raDroads,  254 
Fowler,  Charles  Evan,  139,  234 
Frame  trestles  for  military  bridges,  465 
Fraser  River  Arch  Bridge  at  Lytton,  B.  C, 

249 
Fraser  River  Bridge    at  New  Westminster, 

B.  C,  131 
Fratt  Bridge  at  Kansas  City,  132,  169 
Free  ends  versus  anchored  ends  for  stiffening 

trusses,  268 
Freezing  water,  disruptive  force  of,  455 
Freight  rates,  23 
Friction, 

caisson,  156 
long  piles,  156 
Fuller,  William  B.,  389 
Full-punched  work,  211 
Full  time  work,  necessity  for,  2 
Function  of  operating  machinery,  315 
Future,  anticipating  the,  16 
Future  enlargement,  121 


G 

Galveston  Causeway,  140 

Gardiner,  J.  B.  W.,  449 

Gardiner  and  Lewis,  Inc.,  449 

Gas,  effects  of,  on  steel,  416 

Gases,  locomotive,    protection    against,    444 

Gasoline  engine,  multi-cylinder,  313 

Gauntleted  tracks,  128 

Gearing, 

elimination  of  noise  of,  313 

spur,  312,  313 

worm,  313 
General  economic  principles,  6 
General  features  of  structure,  120 
Geographical  conditions,  119 
Girders, 

depths  in  viaducts,  203 

economics  of,  175-181 

erection  of,  397 

reinforced-concrete,  221,  223-225 

spacing  of,  191 
Glasgow,  Missouri  River,  Bridge,  168 
Goheen's  Carbonizing  Coating,  432 
Gorge    crossings    are    specially    suitable    for 

arches,  246 
Government  requirements,  116,  117 
Grade  and  alignment,  118,  119 
Grant,  General,  crossing  of  the  James  River 

by,  471 
Gratis  expert  opinion,  7 
Gravel    and    sand    used    without    screening, 

390 
Great  Miami  River  Bridge,  84 
Griest,  Maurice  E.,  256 
Growth  of  steel,  215 
Gunite,  443 


H 

Hadfield,  Sir  Robert,  36 

Half  pin  holes,  216 

Half-through,  plate-girder  spans,  185 

economics  of,  69 
Halsted-Street  Lift-Bridge,  294 
Hamilton    Arch    Bridge    over   the    Waikato 

River,  246 
Handling  of  work  in  shops,  368,  369 
Handrails,  190,  219 

military  bridges,  474 
Hand  riveting,  207 
Harbor  of  refuge,  318 
Hardesty,  Shortridge,  297 
Harper's  Ferry  crossing  of  the  Potomac,  471 
Harrop,  Dr.  H.  B.,  440 
Havana  Harbor  bridge,  proposed,  332 

transbordeur,  proposed,  332-334 
Havre  de  Grace,  Md.,  paint  experiments,  433 
Hayde,  Stephen,  198 
Haydite,  198 
Heat  for  shops,  367,  368 
Heat-treated  steel,  37 

intensities  of  working  stresses  for,  37 
Heel-counterbalanced-trunnion  type  of  bas- 
cule, 290 
Heel-trunnion  bascule,  297 
Height  from  springing  to  bottom  of  base,  226 
Height  of  climb  over  a  bridge,  54 
Helpers,  low-grade,  380 
Heritage,  Carl  S.,  407,  418 
High  bridge  versus  low  bridge,  12 
High-carbon  steel, 

objections  to,  33 

reinforcing  bars,  133 
High-level  bridge  versus  transbordeur,  330 
High  level  versus  low  level  crossings,  61,  62,  63 
High  steel,  34 

reinforcing,  objections  to,  218 
High  unit  stresses,  133 
High  water,  clearances  above,  122 
Highway, 

girder-bridges,  223-225 

live  loads  for,  126 

trestles,  economic  span-lengths  of,  252 
Highway  bridges, 

decks  of,  187 

timber  versus  concrete  for,  187 

economics  of  cantilever  and  suspension, 
106 

econoinics  of  continuous  spans  for,  78 

floors,  ties  in,  192 

floor-systems  of,  190-200 
Hildreth  &  Company,  361 
"Hillside"  blocks,  426 
Hingeless  arches,  237 

three-hinged  arches  comparison,  229 
Hinge  plates,  216 
Holding  power  for  bascules,  316 
Holland,  Chfford  M.,  56 


500 


INDEX 


Hollow  shafts,  168 

Home  office,  reports  for,  380 

Honningen  crossing  of  the  Rhine,  471 

Hoogly  River  bridge  at  Calcutta,  proposed, 

296 
Horse-propelled  vehicles,  21 
"Hospital  jobs,"  341 
Housa tonic  River  bascule  bridge,  298,  308, 

309 
H-section  for  posts,  200 
Hudson  River  crossing  at  New  York  City,  58 

railway  bridge,  uneconomics  of,  60 
Hudson  River  Tunnels,  56 
Huntington,  ColHs  P.,  12 
Hydrated  lime,  391,  457 
Hydraulic  power  for  bridge  operation,  311, 

312 
Hydraulic  reducing-gear,  313 


Ice-breakers,  169 
Ice  drift,  122 
Ideal, 

method  of  contract-letting,  344;  345 

operating  apparatus,  313 

shop  coat  of  paint,  432 

system  of  contract-letting,  343,  344 
Idleness,  366 

Ignoring  of  impact  on  foundation  piles,  140 
Illinois    Central    Railroad    Bridge    at    East 

Omaha,  22 
Impact, 

allowances,  latest  modifications  of,  127 

foundation  piles,  140 

old  bridges,  412 
Improvisation  in  military  bridging,  47!S,  479 
Inclination  of  lacing  bars,  207 
Increasing  fluidity  of  mixture  of  concrete,  391 
Increasing  national  efficiency,  2 
Indices,   card,  360 
Infrequent  loadings,  133 
Inspecting  Bureaus  and  Engineers,  362 
Inspection, 

compensation  for,  361,  362 

damages  for  faulty,  362 

economics  of,  361-363 

economics  of  mental  effort  as  applied  lo, 
364 

field,  364 

force,  363 

importance   of  having  it  properly  done, 
304 

methods  of  payment  for,  362 

military  bridges,  4S5 

omission  of  is  uneconomic,  362 

periodical,  419 

quality  of,  361 
Inspectors,  fitness  of,  363,  364 
Instnictions  to  resident  engineer,  380 
Instruments,  surveying,  382 


Intensities  of  working  stresses 
concrete,  219 
heat-treated  steel,  37 

tension  and  compression,  relation  of,  136 
Intermediate  trusses  and  cables  for  suspen- 
sion bridges,  264 
Intermediate  trusses  for  cantilever  bridges, 

260 
Investigation,  principle  of  economic,  6 


Jack-stringers,  184,  185 

James  River  crossing  by  General  Grant,  471 

Japan  oil,  Sipe's,  436 

Jigging  of  freshly  made  concrete,  392,  393 

Joints  and  fastenings  of  military  bridges,  476 


K-truss,  71 

Kansas  City  bridge  over  Missouri  River,  132 
Kansas  City  elevated  railroad,  defective,  74 
Kansas  University,  lectures  on  engineering 

economics,  4 
Keeping  employees  busy,  380 
Knowledge,  collection  of,  365 


Labor, 

a  blessing,  1 

facilities,  123 

handling  of,  19 

material  versus,  18 

military  bridges,  478 

rise  in  price  of,  348 

supply  of,  373 
Labor  and  capital,  338 
Lacing  bars,  inclination  of,  207 
Lacing  versus  tie  plates   in   riveted   tension 

members,  207 
Lambrecht,  Jules,  35 
Lamps,  electric,  in  shops,  367 
Large  stones  in  mass  of  concrete,  392 
Lashings,  476 

Lateness  of  starting  work,  358 
Lateral  system,   dropping  of,  for   clearance, 

206 
Latin  America  asking  for  business,  2 
Layouts, 

determination  of,  116-124 

factors  and  conditions  affecting,  116 

fieldwork,  380 
Leaching  of  concrete  by  iiercolation  of  wat(>r, 

454 
Le  Genie  Civil,  26 
Leiter's  Air-Drying,  Salt-Water-Proof  paint, 

439 
Lengths    of    panels    for    rcinforccd-concrete 

girders,  224 
Lettering,  359 
Lcucol  oil,  435 


INDEX 


501 


Levees,  122 
Life, 

metal  bridge,  430 

reinforced-concrete  bridges,  64 

steel  bridges,  64 

water-proofing,  probable,  451 
Lift  bridges, 

automatic  brakes,  295 

balancing  chains,  294 

base  for  pavement,  295 

buffers,  295 

location  of  machinery  house,  295 

quantities,  299 

records,  297 
Light, 

beneficial  effects  of,  367 

shops,  367 
Light  bridges,  strengthening  of,  416,  417 
Light  structure  at  outset,  economics  of,  16 
Lime,  hydrated,  391,  457 
Limiting  span-length, 

inferior  for  pin-connected  bridges,  74 

reinforced-concrete  bridges,  66 

steel  arches,  241 
Limits,  economic,  wide  range  of,  16 
Lindenthal,  Dr.  Gustav,  75,  437 
Linseed  oil, 

alone  for  shop  coat,  438 

boiled,  435 
List  of  author's  writings  on  bridge  economics, 

489,  490 
Litharge,  434 

Little  Pedee  River  crossing,  472 
Live  loads,  125-127 

cantilever  bridges,  127 

combined  bridges,  132 

decreasing  with  span-length,  125 

determination  of,  13,  125 

excessive,  125 

highway,  126 

steam  railway,  126 
Loadings, 

abnormally  heavy,  133 

auto-truck,  125 

classification  of,  412 

deep  foundations,  156 

electric  railway,  126 

future  additions  to,  16 

highway,  126 

infrequent,  133 

military  bridges,  481 

standard,  for  old  bridges,  411 

steam  railway,  126 

Train,  Classification  of,  413 
Loads  and  unit  stresses,  economics  of,  125- 

140 
Local  resources,  utilization  of,  480 
Location, 

bridge,  effect  of,  on  economics,  25 

machinery  house  for  lift  bridges,  295 


Location, 

sidewalks,  195 
top-chord  pins,  204 

Locomotive  gases,  protection  against,  444 

Log  books,  381 

Logs,  sunken,  172 

Longitudinal  girders,  spacing  of,  224 

Loose  plates  to  be  avoided,  217 

Loose  rivets,  423 

Love  for  work,  1 

Lowe,  Houston,  433,  444,  446 

conclusions  concerning  paint,  433 
opinion  of  concerning  the  desirable  fea- 
tures of  an  anti-corrosive  metal 
coating,  434 

Loweth,  Charles  F.,  407,  409 

Low  bridge  versus  high  bridge,  12 

Low  classification  for  old  bridges,  414 

Low  level  versus  high  level  crossings,  61,  62, 
63 

Lubrication,  314,  315 

Lumber,  treated,  unsatisfactory  for  floor,  426 

Lump  sum  contracts,  340 
objections  to,  340,  341 
suitable  only  for  war  times,  341 

Lytton  arch  bridge  over  the  Fraser  River,  246 

M 
Machinery, 

breakdowns  of,  315 

definition  of,  314 

house  for  lift  bridges,  location  of,  295 

operating,  economics  of,  310-317 
function  of,  315 

power  operation  versus  operation  by  hand, 
386 

shops,  378 

steel,  34 

utilization  in  shopwork,  202 
Machine  shop,  378 

work  to  be  minimized,  211 
Machines,  scrapping  of  old,  367 
Magnesia,  excrescence  of,  456 
Maintenance, 

floors,  425 

masonry,  424 

operation,  capitalization  of,  15 

repairs,  124 

economics  of,  407-429 
Maintenance  of  bridges, 

economic  consideration,  410 

safety  consideration,  410 
Management  of  men  in  shops,  368,  369 
Manner  and  time  of  mixing  concrete,  391 
Man-power,  366,  386 
Manufacture  of  concrete,  economic  problems 

in,  387 
Manufacturers'  standards,  205 
Market  price  variations,  effect  of,  23 
Marking  metal,  374 


502 


INDEX 


Masonrj^  maintenance,  424 
Masonry  piers,  167 
Masonry,  stone,  repairs  to,  420 
Materials  and  supplies,  384 
available,  484 

best  proportions  of,  for  concrete,  387-389 
checking  of,  380 
counterweights,  294 
employed  in  miHtary  bridging,  474 
purchasing  cheaply,  386 
quick  ordering  of,  385 
special,  for  contracts,  373 
stock,  372 
storage  of,  382,  386 
unloading  of,  380,  381 
versus  labor,  18 
versus  time,  18 
Mathematics  in  bridge-economics  investiga- 
tions, 175 
Mattress  work,  122 

woven  brush,  474 
Mayari  steel,  33,  34 

cables,  279 
Medium  spans,  erection  of,  399 
Members  in  military  bridges,  sizes  of,  477 
Men, 

management  of,  368,  369 
treatment  of,  385 
Mental  effort,  economics  of,  18 

as  applied  to  inspection,  364 
Merriman  and  Jacoby's  treatment   of  canti- 
lever bridges,  261 
Metal, 

cleaning  of,  422,  445 
for  shop  coat,  441 
life  of,  430 
marking  of,  374 
minimum  thickness  of,  201 
protection,  economics  of,  430-448 
storage  of,  376,  441 
straightening  of,  374 
structural,  prices  of,  23 
trimming  and  cutting  of,  374 
"Metalcote, "  432 
Methods, 

comparison,  14 
contract-letting,  339,  340 
erection,  123 

profit-sharing  contract,  345,  346 
Military  bridges, 
bolts,  477 
classes  of,  463 
concrete,  476 
deck  or  flooring,  474 
economics  of,  459-485 
improvisation  in,  478,  479 
inspection,  485 
joints  and  fastenings,  476 
labor,  478 
lack  of  strength,  459 


Military'  bridges, 
loading,  481 
paint,  476 
piling,  475 

plant  and  tools,  464,  477 
standardization,  478,  479 
steel,  475 
stone,  476 
timber,  475 

transportation  of  materials,  482 
types,  464 
typical,  465 
waste  not  justified,  462 
Mill  inspection,  363 
Milling  and  planing,  377 
Minimum  thickness  of  metal,  201 
Mississippi  River  Bridge,  economic  study  for 

replacement  of,  13 
Mississippi  River  bridge  or  tunnel  at  or  near 

New  Orleans,  296,  319 
Missouri  River  Bridges, 
East  Omaha,  131 
Fort  Leavenworth,  repairs  to,  408 
Sioux  City,  131 
Missouri  Valley  Bridge  Company,  439 
Mixed  carbon  and  alloy-steel  bridges,  30 
Mixing  concrete, 
economics  of,  386 
increasing  fluidity  of  mixture,  391 
manper  and  time  of,  391 
water,  amount  of,  392 
Moisture  changes,  provocative  of  cracks  in 

concrete,  456 
Molybdenum, 
as  an  alloy,  34 

economic  benefit  from,  in  steels,  44 
gain   involved   by  increasing   percentage 
of,  49 
Molybdenum  steel,  36 
bridges,  use  in,  487 
Commercial  Steels  (catalogue) ,  36 
economic  comparisons  of,  44-51 
tests  of,  38-43 
Monthly  estimates  to  be  made  promi)lly,  3M 
Montreal  enterprise,  7 
Motive    power    dependent    on    location    of 

structure,  310 
Movalile  bridges, 

comparative  costs  of  various  typos  of,  297 
economics  of,  284-309 
effect  of  wind  pressure  on,  293 
examples    illustrating    use    of    economic 

curves  for,  304-30S 
main  elements  in,  314 
pavements  for,  293 
quickness  of  operation  in,  293 
skew  layouts  for,  303 
Multi-cylinder  gasoline  engine,  313 
Mulfiple  punches,  375 
effect  of,  206 


INDEX 


503 


Mystic  River,  Brown  balance-beam  bascule 
bridge,  291,  298,  308 

N 
National  Economic  League,  4 
National  efficiency,  increasing,  2 
Nature  of  banks  and  approaches,  483 
Nature  of  bottom,  483 
Navigation  influences,  123 
Necessity  for  economic  studies,  7 
New  Orleans, 

bridge  project,  12 

bridge  studies,  151,  155 

proposed  bridge,  296 

report,  8,  319 

transbordeur,  description  of,  321-323 
New  types  of  ponton  equipage,  472 
New  Westminster,  B.  C,  bridge  over  Fraser 

River,  131 
Nichro  steel,  37,  48 

Nichromol  steel  comparison,  47 

tests  of,  39 
Nichromol  steel,  34,  37,  48 

Nichro  steel  comparison,  47 

tests  of,  39 
Nickel- chromium-molybdenum  steel,  37 
Nickel-molybdenum  steel,  37 
Nickel  price,  as  affected  by  Great  War,  33 
"Nickel   Steel  for  Bridges,"  91 
Nickel  steel,  26,  47 

bridges,  use  in,  33 

cables,  280,  281 

floor-systems,  31 

Nicmol  steel  comparison,  46 

tests  of,  41 
Nicmol  steel,  37,  47 

Chromol  steel  comparison,  51 

nickel  steel  comparison,  46 

tests  of,  41 
Nobrac,  432 

Noise  of  gearing,  elimination  of,  313 
Non-continuous    versus    continuous    trusses, 

75-82 
North  River  crossing  at  New  York  City,  58 

highway  tunnels,  56 

proposed  bridge  for  railway  and  highway 
traffic,  60 
Northwestern  Elevated  Railroad,  253 
Number  of  columns  per  bent,  best,  224 

O 

Objections  raised  to  proposed  ideal  method  of 

contract-letting,  354-356 
Obstruction  of  waterway  by  pier  shafts,  170 
Office  work,  economics  of,  358-360 
Old  bridges, 

doubling-up  of,  407 

pins  in,  415 

rule  for  condemnation  of,  407 

strengthening  of,  409 


Omission  of  end  floor  beams,  203 
Omissions,  avoidance  of,  20 
One-man  stones  in  concrete,  386 
One-way  versus  two-way  reinforcing  in  slabs, 

220 
Open-dredging  and   pneumatic   methods   on 

same  job,  173 
Open-dredging  versus  cofferdam  method,  171 
Open-dredging  versus  pneumatic  i^rocess,  171 
Open  spandrel  versus  solid  spandrel,  228 
Open  timber  decks,  184 
Open-web  girders  versus  plate-girders,  255 
Open-web  riveted  spans,  economics  of,  70 
Operating  apparatus,  ideal,  313 
Operating  bridges  by  hydraulic  pressure  or 

compressed  air,  311 
Operating  machinery  and  power,  economics 

of,  310-317 
function  of,  315 
power  of,  315 
strength  of,  315 
Operation    and    maintenance,    capitalization 

of,  15 
Operation  costs  of  tunnels  and  bridges,  55 
Opinion,  expert,  gratis,  7 
Opposition  of  rival  promoters,  20 
Optimism,  20 

Ordering  quickly  of  materials,  385 
Ordinary  swing  versus  bob-tailed  swing,  288 
Organization,  field,  383 
Overestimating,   20 
Overloading  of  bridges,   13 
Over-stressing  counters,  423 


Paints  and  Painting,  379 
abrasion,  445 
accessibility  for,  201 
application,  422 

after  cleaning,  446 
best  colors,  436 
best  kind,  430,  431 
cement,  437 

climatic  influences,  421,  438,  440 
colors,  428 

comparative  cost  of  application,  421 
correct  and  economic  theory  of,  448 
covering  power,  436 
deterioration,  causes  of,  444 
economics  of,  430-448 
elasticity,  436 

experiments  at  Havre  de  Grace,  433 
factors  that  affect  results  in,  446 
fire-proof,  420 
for  steel  bridges,  421 

general   economic   observations   concern- 
ing, 447 
highway  bridges,  427 
importance,  421 
incipient  failure,  445 


504 


INDEX 


Paints  and  painting, 

interior  of  shop  white,  367 

layers,  thickness,  447 

Leiter's    Air-Drying,     Salt- Water-Proof, 
4.39 

Lowe's  conclusions  concerning,  433 

military  bridges,  476 

mixing,  432 

newly-erected  steelwork,  442 

paste  form,  432 

powder  form,  432 

price,  447 

priming  coats,  422 

program,  428 

recommendation  of,  by  engineers,  431 

spraying,  422,  440 

spreading  power,  436 

summary  of  author's  conclusions  concern- 
ing, 448 

temperatures  suitable  for,  448 
Panel  lengths,  economic,  179,  209 

for  suspension  bridges,  265 

reinforced-concrete  girders,  224 
Parallel  chords,  economic  truss   depths  for, 

176 
Parallel     chords    versus     polygonal    chords, 

180 
Pasadena,   Calif.,   bridge  over  Arroyo  Seco, 

248 
Pavements,  187,  188,  219 

asphalt,  188 

base  on  lift  bridges,  295 

bitulithic,  188 

bituminous,  188 

concrete,  188 

expansion  joints  for,  219 

movable  spans,  293 
Paving  blocks,  storage  of,  382 
Paying  enterprises,  8 
Pedestals, 

bases,  plain    concrete    versus    reinforced, 
173 

cantilever  bridges,  260 

costs     affecting    economic    layouts     for 
trestles,  252 
Pedestrian  traffic  on  transbordeur,  323 
Pedestrian  travel,  21,  128 
Penalizing  a  contractor,  340 
Percentage  of  profit  for  employees,  348 
Percolation  of  water  through   concrete,   454 
Permanence   negligible   in   military    bridges, 

462 
Permissible  pressures  on  soil  and  piles,   155 
Personal  equation  in  designing,  05 
Petit  trus.ses  for  continuous  spans,  78,  81 
Petit  versus  Pratt  trussing,  71 
Philadelphia-Camden      Suspension      Bridge, 
proposed,  270,  318 
( riuisbordour,  fn'oposod,  .335 
PickMng  f)f  metalwork,  442 


Piers, 

minimum  expense  for,  57 
temporary,  in  Missouri  River,  168 
two-pedestal,  94 
Pier-shafts, 

aesthetics,  168 
cocked-hat,  169 
depth  below  water,  170 
reinforcing  of  concrete,  167 
'  Pigments,  character  of,  448 
Piles, 

buUt,  296 

cribs  versus  caissons,  173 
foundations  for  arches,  244 
friction,  156 
impact,  140 

loading,  permissible,  155 
military  bridges,  475 
piers  under  steel  spans,  169 
reinforced-concrete,  225 
steel  sheet,  171,  172 
trestles  for  military  bridges,  467 
trestles,  replacing  of,  419 
wooden  versus  reinforced,  174 
Pin  bearings,  wear  in,  415 
Pin-connected    bridges,    inferior   span-length 

for,  74 
Pin-connected  elevated  railroads,  73 
Pin-connected  versus  riveted  bridges,  72 
Pin  holes,  half,  216 
Pins, 

cost  of  shopwork  on,  73 
old  bridges,  415 
sizes,  207 

top  chords,  location  of,  204 
wear,  423 
Plain  concrete  versus  reinforced-concrete  for 

pedestal  bases,  173 
Planing  and  milling,  377 

sheared  edges,  202 
Plank  floors,  undesirable,  425 
Planning  system  for  shops,  379 
Plant,  384 

erection,  402,  403 
military  bridges,  464 
tools  for  militarj^  bridges,  477 
Plate-girders, 

cambering,  207 
criterion  for  alloy  steels,  27 
deck,  economics  of,  68 
economic  depths  of,  178-180 
half-through,  185 

economics  of,  09 
open-web  girder  comparison,  255 
round  corners  in,  207 
Plate-lattice-girder  spans,  70 
Plates, 

loose,  to  bo  avoided,  217 
standard  dimensions  for,  205 
Platforms  for  cleaners  and  painters,  446 


INDEX 


505 


Pneumatic   and   open-dredging  methods  on 

same  job,  173 
Pneumatic  process  versus  open-dredging,  171 
Polygonal  chords  versus  parallel  chords,  180 

economic  depths  of  trusses  with,  176,  177 
Ponton  equipage,  new  types  of,  472 
Ponton  or  floating  bridges,  470 
Portable  drills,  379 
Possibilities    and    economics    of    the    trans- 

bordeur,  318-336 
"Possibilities  in  Bridge  Construction  by  the 

Use  of  High-Alloy  Steels,  "91 
Posts,  H-section  for,  200 
Potomac  River  crossing  at  Harper's  Ferry, 

471 
Pound  prices  for  various  sections,  205 
Power, 

arbitrary,  of  resident  engineer,  382 

conveyance  of,  312 

cost  of,  55 

crossing  bridges  and  tunnels,  54,  55 

economics  of,  310-317 

efficiency,  definition  of,  311 

hydraulic,  311,  312 

operating  machinery,  315 

shop  operation,  366 

steam,  for  bridge  operation,  311 

type  of,  dependent  on  location  of  struc- 
ture, 310 
Pratt  versus  Petit  trussing,  71 
Pratt  versus  triangular  trussing,  71 
Pre-moulded  slabs,  230 
Preservation  of  timber,  419 
Prevention  of  progress,  338 
Prices, 

alloy  steels,  44 

alloy  steel  constituents,  44 

structural  metal,  erected,  23 

suspension  bridges,  25 

unit,  for  bridges,  57 

variations,  effect  of,  23,  24 
Priest,  H.  Malcolm,  75 

Primary  truss  members,  criterion  for  econom- 
ics of,  26 
Priming  coats  of  paint,  422 
Principles, 

economic    investigation     of    engineering 
practice,  6 

general  economic,  6 

of  true  economy,  importance  of,  1 
Probable  life  of  water-proofing,  451 
Probable  traffic,    20 

Problems,  economic,  in  manufacture  of  con- 
crete, 387 
Profit,  percentage  of  for  employees,  348 
Profit  sharing,  338,  343,  370 

employees  of  manufacturers,  357 

method  of,  345,  346 
Progress, 

prevention  of,  338 


Progress, 

reports  and  charts  of,  381 
Promotion  of  bridge  projects,  20 
Property  considerations,  120 
Property  (field)  of  the  engineers,  381 
Proportions  for  concrete,  387 
Proposed, 

enterprise,  economics  of,  7 

railroad  economics,  15 
Protection, 

against  brine  drippings,  443 

against  flood  and  drift,  485 

against  locomotive  gases,  444 

cement,  382 

fresh  concrete,  394 
Protrusion  method  of  erection,  399 
Public   Belt   Railroad    Commission    of   New 

Orleans,  320 
Punch  Shops,  375 
Punched  metal,  storage  of,  376 
Punching,  375 

full  size,  202 
Purchasing  Agent,  384 
Purchasing  of  materials  cheaply,  386 
Purified  steel,  33,  34 


"Quality  Number,"  44 

Quantities, 

vertical  lifts  and  bascules,  299 
wire-cable  suspension-bridges,  276 

Quebec  cantilever  bridge,  30,  71,  132 

Queensboro  Bridge,  195 

Quick,  Howard  P.,  440 

R 

Railroads, 

bridges,  electric,  187 

economics  of,  6,  15 

elevated,  253 

economics  of,  250-256 

miUtary  bridges,  473 

trestles,  economics  of,  250-256 
Rails  laid  directly  on  steel  work,  183 
Rails  resting  on  steel  floor,  186 
Range  of  economic  limits,  16 
Ratios, 

cost  of  fixed-span  bridges  and  their  ap- 
proaches for  various  clearances 
above  high  water,  331 

rise  to  span,  225,  233-235 
Reaming,  376 

subpunching-versMs  punching  full  size,  202 

templets,  205,  215 
Recommendation  of  paints  by  engineers,  431 
Recording  diagrams,  18 
Records, 

cost,  360 

floors,  427 


506 


INDEX 


Records, 

unit  costs,  385 

weights  of  lift  bridges,  297 
"  Red  Lead  Lute, "  432 
Red  lead, 

paint  for  shop  coat,  431 

proportion  of,  in  paint,  434 
Red  Oxide  No.  31,  432 
Red   Rock   Cantilever   Bridge,    designing   of 

piers  for,  167 
Reduced  live  loads  for  combined  bridges,  132 
Reducing-gear,  hydraulic,  313 
Reduction  of  voids  in  the  aggregate,  389 
Reichmann,  Albert,  214 
Reinforced-concrete, 

bridges, 

arch  bridges,  225-230 
economics  of,  218 
Hfe  of,  64 

limiting  span-length  of,  66 
small  cost  of  maintenance  and  repairs 
for,  64 

caissons,  169 

columns,  223 

girders,  221,  223-225 

pier-shafts,  167 

piles,  225 

piles  versus  wooden  piles,  174 

steel  structures,  64 

trestles  for  steam  railways,  230 

trestle  versus  steel  trestle,  114 

versus  plain  concrete  for  pedestal  bases, 
173 

viaducts,  water-proofing  for,  454 
Reinforcing  bars,  high-carbon  steel  for,   133 
Reinforcing  steel,  218 

Repainting,  determination  of  time   for,   445 
Repairs,  124 

economics  of,  407-429 

renewals,  equipment  for,  420 

stone  masonry,  420 

timber  bridges,  419 
Replacing, 

long  spans,  405 

short  spans  on  old  substructure,  404 

steel  bridges,  403,  404 
Report, 

author  to  S.  P.  E.  E.,  3 

home  office,  380 

progress,  381 
Requirements  of  U.  S.  Government,  116 
Resident  engineer, 

arbitrary  power  of,  382 

decisions  by,  381 

instructions  to,  380 
Resistance  of  brakes,  315 
Restrictions  of  speed,  412 
Retaining  walls,  231 
Revenue,  sources  of,  20 
Reversal  of  current,  122 


Reversing  stresses,  135 

effect  of,  on  continuous  trusses,  77 
Rhett,  Albert  H.,  458 
Rhine  crossing  near  Honningen,  471 
Ribbed  structure  versus  solid  barrel,  228,  229 
Rib  depths,  economic,  235,  236 
Rice,  Geo.  S.,  433 
Right-of-way,  cost  of,  114 
Rim-bearing    versus     center-bearing     swing- 
spans,  287 
Rip-rap,  122,  424 
Rise, 

arch,  226 

economic,    of    suspension    bridge    cables, 
265,  266 

ratio  of,  to  span,  233-235 

with  span-length  unchanged,  225 
Rise  in  price  of  labor,  348 
Risk,  assumption  of,  340 
Rivalry  in  bridge  projects,  20 
River  traffic,  123 
Riveted  spans,  economics  of,  70 
Riveted  tension  members,  199 
Riveted  versus  pin-connected  bridges,  72 
Riveting, 

arrangement  of,  199 

machines,  377 

sequence  of,  214 

staggered,  211 
Rivets,    . 

loose,  423 

spacing,  210 
Roads,  drainage  of,  454 
Roadwaj^s, 

crowning  of,  426 

widths,  127 

widths  for  military  bridges,  473,  474 
Rolled  I-beam  spans,  economics  of,  67 
Roller-bearing  bascules,  290 
Rolling-lift  bascules,  290 
Roof  protection  for  timber  bridges,  420 
Round  corners  in  plate-girders,  207 
Rusting  as  affecting  detailing,  201 

S 
Sabin,  Dr.  A.  H.,  433,  436-438 
Safety  and  permanence  in  military  l)ridges, 

462 
Safety  considerations,  370 
Safety  factor  small  in  military  bridges,  462 
Salary  for  contractor,  objoctional)lp,  348,  349 
Sand  and  gravel  used  without  screening,  390 
San  Francisco  Harlior  Bridge,  proposed,  8,  10 
Sanitation  of  liridges  and  tininels,  56 
Scamping  work,  342 
Scarcity  of  timl)er,  growing,  22 
Schedule  pric^os  for  various  sections,  205 
Schneider,  C.  C.,  287 
Sciotoville  bridge,  75,  77 
Scour,  122.  424 


INDEX 


507 


Scrapping  old  machines,  367 

Screens  between  railway  and  highway  traffic, 

129 
Sealing  cofferdams,  172 
Secondary  stresses,  72,  73 

intensities  of  working  stresses  for,  136 
Second  Narrows  proposed  bridge,  Vancouver, 

B.  C,  131 
Secrecy,  484 
Sectional    trusses    and    girders    for    military 

bridging,  468 
Sections, 

columns,  best,  255 

floor  beams,  186 

stringers,  186,  206 
Selection  of  site  for  military  bridges,  483 
Seltzer,  Harry  K.,  383 
Semi-cantilevers,  83 

Semi-can tilevering  of  continuous  trusses,  81 
Separation  of  entrances  and  exits,  55 
Shafts, 

depth  below  water,  170 

hollow,  168 

proportioning,  167 
Sharing  of  profits  with  workmen,  370 
Sheared  edges,  planing  of,  202 
Sheet  piling,  steel,  171,  172 
Shelf  angles,  184 
Shelves,  214 

Shifting  of  channel,  122,  293 
Shop, 

accidents,  370,  371 

assembling,  378,  379 

blacksmith,  378 

coat,  cleaning  of  metalwork  for,  441 

coat,  red  lead  paint  for,  431 

considerations,  209 

economics  in  designing  for,  202—213 

designing  to  suit  fabrication,  366 

drawings,  210 

should  not  be  prepared  in  Consulting 
Engineer's  office,  359 

electric  lamps,  367 

floors,  374 

handling  of  work,  368,  369 

heat,  367,  368 

inspection,  363 

light,  367 

machinery,  378 

management  of  men,  368,  369 

operation,  power  for,  366 

painting  interior  white,  367 

size  of  force,  380 

smoking,  371 

space,  367,  368 

special  space,  377 

standardization,  372 

storage  ground,  373 

tracks,  379 

ventilation,  367,  368 


Shopwork, 

cost  on  pins  and  holes,  73 

economics,  365-379 

general  economic  problem,  365,  366 
Short  cuts  in  computing,  92 
Side  friction  on  caisson,  156 
Side  plates,  avoidance  of,  206 
Side  rails  of  military  bridges,  474 
Sidewalks,  189,  195 
Silicon  steel,  33,  34 
Simple-truss  bridges, 

cantilever  bridge  comparison,  83-89 

economic  limit  of  length  for,  84 

economic  span-lengths  for,  17,  150-165 
Simple  versus  continuous  reinforced-concrete 

girders,  221,  222 
Single  angles  in  tension,  204 
Single-leaf  versus  double-leaf  bascule,  289 
Sioux  City  Bridge  over  Missouri  River,  131 
Sipe's  Japan  oil,  436 
Site  selection  for  military  bridges,  483 
Sizes    of    individual    members    in    military 

bridges,  477 
Skew  layouts  for  movable  spans,  303 
Skewed  crossings  for  vertical  lifts,  293 
Skewed  spans,  209 
Skids,  376,  377 
Skimping  details,  133,  201 
Skimping  reinforcing  of  girders,  222 
Skinner,  Frank  W.,  396 
Slabs, 

continuity,  221 

designing,  220 

pre-moulded,  230 

steel,  arrangement  of,  220,  221 

supporting,  193 

water-proofing,  454 
Smoke  effects  on  steel,  416 
Smoking  in  office,  358 
Smoking  in  shops,  371 

Society   for   the    Promotion   of   Engineering 
Education,  3 

author's  report  to,  on  study  of  econom- 
ics, 3 
Soil  pressure,  permissible,  155 
Solid-barrel  arches,  227 

ribbed  arch  comparison,  228,  229 
Solid  drilling,  208 
Solid-slab  trestles,  230 
Solid  spandrel  versus  open  spandrel,  228 
Solitary  columns  versus  braced  towers,  254 
Solitary  piers  for  cantilever  bridges,  260 
Soundings  around  piers,  424 
Space  in  shops,  367,  368 
Spacing, 

columns  in  bents,  253 

longitudinal  girders,  224 

rivets,  210 

stringers  and  cross  girders,  192,  194 

trusses,  186 


508 


INDEX 


Spacing-tables,  375 
Spandrel-braced  arch,  237 
Span-lengths, 

arches,  inequality  in  length  of,  227 
economic, 

cantilever  bridges,  258 
determination  of,  17,  158 
elevated  railroads,  254,  256 
for  trestles,  250-256 
rise  unchanged,  226 
simple-truss  bridges,  17,  150-165 
tabulation  of,  160 
effect  on  comparative  economics  of  steel 
and    reinforced-concrete    struc- 
tures, 66 
limiting,  for  steel  arches,  241 
Spans  without  floor  systems,  183 
Spar  bridges,  466,  467 
Special  material  for  contracts,  373 
Special  material  to  be  avoided,  205 
Special  space  in  shops,  377 
Specifications,  standardization  of,  372 
Speculative  zone,  30 
Speed  restrictions,  412 
Speeds  for  maximum  impact,  414 
Spiral  approaches,  59,  114 
Splaying  of  trusses  in  cantilever  bridges,  260 
Splices  in  webs,  207 
Spraying  of  paint,  422,  440 
Spreading  power  of  paint,  436 
Springings,  arch,  226 
Spur  gearing,  312,  313 
Staggered  riveting,  211 
Standard, 

apparatus,  use  of,  316 
dimensions  for  plates,  205 
loadings  for  old  bridges,  411 
parts,  importance  of  using,  359 
Standards  of  bridge  manufacturers,  205 
Standardization, 
bridges,  372 

military  bridging,  478,  479 
shops,  372 
specifications,  372 
Stay  plates  inside  of  gussets,  203 
Steam  power  for  bridge  operation,  311 
Steam  railways, 
electrified,  126 
loadings,  126 

reinforced-concrete  trestles  for,  230 
Steel, 

arches, 

economics  of,  232-249 
limiting  span-length  for,  241 
tabulation  of  salient  features  of,  234 
bottom     chords     in      reinforced-concrete 

arches,  229 
bridges, 

comparative    (■(•nnoniics    of    different 
types  of,  67 


Steel, 

Ufe  of,  64 

replacing  of,  403,  404 
cylinder  piers,  168 
forms  for  concrete  compared  with  timber, 

170 
growth  of,  215 
military  bridges,  475 
sheet  pihng,  171,  172 

structures,  prevention  of  corrosion  in,  421 
treatment  of,  for  encasement,  443 
trestles, 

columns,  method  of  proportioning  of, 

134 
economics  of,  250-256 
reinforced-concrete     trestle     compari- 
son, 114 
Steel  versus  reinforced-concrete  structures,  64 
Steinman,  Dr.  D.  B.,  90,  91,  95-106 
Stiffened  buckle-plate,  195 
Stiffening  angles,  fitting  of,  203,  212 
Stiffening  trusses,  anchored  versiis  free  ends, 

265,  268 
Stiffening  trusses  for  suspension  bridges,  265 

formula  for  weights  of,  93 
Stitch  rivets,  208 
Stock  materials,  372 
Stone  in  military  bridges,  476 
Stone  masonry,  repairs  to,  420 
Stone    masonry    versus    concrete   for    piers, 

167 
Stoppage  of  traffic  in  tunnels,  57 
Storage, 

batteries,  312 
explosives,  382 

ground,  divided,  for  shops,  373 
materials,  382,  386 
metal,  441 
punched  metal,  376 
Straightening  metal,  374 
Strauss  bascule,  291 
Stream  conditions,  122 
velocity,  122 
width,  483 
Street  car  traffic,  method  of  supporting,  425 
Strength, 

alloy  steels,  38-43 
operating  machinery,  315 
Strengthening  old  bridges,  409 

light  bridges,  416,  417 
Stresses, 

(combination  of,  133 

cantilever  l)ridges  and  arches,  136 
old  bridges,  415 
reversing,  135 
summitig  up,  135 
Stringerless  tyije  of  floor-system,  193,  194 
Stringers, 

crooked,  466 

depths,  economic:,  185 


INDEX 


509 


Stringers, 

sections,  186,  206 

spacing,  192,  194 
"Structural"  defined,  314 
Structural  metal,  price  of,  23 
Structure,  general  features  of,  120 
Student    competition    on    cost    estimating, 

141,  146-149 
Study  of  engineering  economics,  importance 

of,  3 
Subpaving  or  base,  189 
Subpunching,  211 
Subpunching   and   reaming  versus  punching 

full  size,  202 
Substructure, 

economics,  167—174 

influence  on  arch  economics,  238-243,  245 
Sunken  logs,  172 
Superintendent,  383 
Supplies,  384 

availability  of,  123 
Supply  of  labor,  373 
Supporting, 

cables  for  vertical-lift  bridges,  295 

machinery  parts,  314 

structure,  314 
Surveying  instruments,  382 
Surveys,  copying  of,  from  field  books,  381 
Suspended    span  in  cantilever   bridges,  eco- 
nomic lengths  of,  258 
.  Suspending  floor  from  backstays,  266 
Suspension  bridges,  25 

anchorages,  94,  267 

approaches,  266 

best  system  of  cancellation  for  stiffening 
trusses,  265 

buckle-plate  floor,  263 

cantilever  bridge  comparison,  90-112 

decks,  263 

economic  dimensions,  95 

economics,  263-283 

panel  lengths  in,  265 
rise  of  cables,  265,  266 
truss  depths,  265 

ends  of  stiffening  trusses  free  or  anchored, 
265 

erection,  401 

eye-bar     cable,     quantities     of     various 
materials  in,  278 

floor-system,  263 

formulae  for  weights,  273-275 

intermediate  trusses  and  cables,  264 

legitimate  function,  263 

limiting  -widths  of  structure,  94 

military  bridging,  469 

nickel  steel  floors,  264 

prices,  25 

quantities  for  wire  cables,  276 

stiffening  trusses,  265 

weights  of  alloy-steel  eye-bars,  277 


"Suspension  Bridges  and  Cantilevers — Their 
Economic  Proportions  and  Lim- 
iting Spans,"  90 
Swiftness  of  current,  483 
Swing  spans,  298 

bascule  or  vertical-lift  comparison,   284, 

285 
combined  rim-bearing  and  center-bearing 

type  of,  288 
comparative  economics  of,  308 
economics  of,  287 
Symmetry,  209 

System  of  contract-letting,  ideal,  343,  344 
Systemization,  18 


Tabulation  of  economic  span-lengths,  160 

Tallcing  among  employees,  358 

Technical  book  writing  an  extravagance,  486 

Technical  schools,  study  of  economics  in,  3 

Temperatures  suitable  for  painting,  448 

Templet  shop,  379 

Templets,  reaming  to,  205,  215 

Temporary  bridges,  21 

Temporary  economic  expedients,  15 

Temporary    piers    in    Missouri    River,    168 

Tests, 

alloy  steels,  38-43 

cement,  380 

members  in  full-size  bridges,  138,  139 
Thickness  of  web,  207 
Three-hinged  versus  hingeless  arches,  229 
Three-hinged   versus  two-hinged  arches,  238 
Three-span    structure,    economic    investiga- 
tion of,  165 
Through  bolts  in  military  bridges,  477 
Thrust  of  braked  trains,  140 
Thrust  of  earth,  influence  of,  228 
Tides,  122 

Tie-plates  a  necessity,  182 
Tie-plates    versus  lacing   in  riveted   tension 

members,  207 
Ties, 

highway  bridge  floors,  192 

street  car  traffic,  425 

treated,  economics  of,  182 
Timber, 

bridges, 

fire  protection,  420 
repairs,  419 
roof-protection  for,  420 

decks,  184-195 

concrete    for   highway    bridges,    com- 
parison with,  187 

gromng  scarcity  of,  22 

military  bridges,  475 

prices,  23 

steel  for  concrete  forms,  comparison  with, 
170 

treatment,  183, 188 


510 


INDEX 


Timber, 

trestles,  113-115 
approaches,  21 
filling  up,  113 
low  classification  of,  415 
military  bridges,  465 
Time, 

considerations,  121 

element  in  war,  460 

expenditure  on  approach  grades  to  bridges 

and  tunnels,  56 
factor  substituted  for  cost  factor,  461 
mixing  concrete,  391 
repainting,  determination  of,  445 
required  for  solution    of  economic  prob- 
lems, 33 
schedule  of  fieldwork,  380 
versus  material,  18 
Toch  Bros.,  437 
"TockoUth,"  432,  437 
Tool  equipment,  374 
Tools  for  military  bridges,  477 
Top-chord, 

pins,  location  of,  204 

polygonal,    economic    depths    of    trusses 
with,  176,  177 
Top  flanges,  cover-plates  for,  200 
Torch,  use  of,  for  cleaning  metal,  441 
Towers  for  vertical  lifts,  294 
Tracks,  384 

electric-railway,  190 
gauntleted,  128 
shops,  379 
Traction  loadings  for  old  bridges,  412 
Traffic,  20 

congestion  at  entrance  and  exit,  54 
diversion  of,  during  replacement,  405 
investigations,  20 
pedestrians  on  transbordeur,  323 
probable,  20 

several  kinds  on  one  deck,  128 
tunnels,  stoppage  of,  57 
Trains,  thrust  of  braked,  140 
Transbordeur, 

author's  improvements  on,  320 
comparative    operating     capacity,     328- 

330 
conditions  favorable  for,  330 
description,  318 
efficiency,  330 

general    conclusions    concerning    the  eco- 
nomics of,  335,  336 
Havana  Harbor,  proposed,  332-334 
high-level  bridge  comparison,  330 
improvements  on    present   type  of,  319, 

325-328 
inferior  features  of,  318 
New  Orleans,  description' of ,  321-323 
ordinary,  description  of,  319 
Philadelphia  and  Camden,  proposed,  335 


Transbordeur, 

possibiHties  and  economics  of,  318-336 
summary  of  conclusions  on  economics  of, 

320,  321 
time  schedule,  324 
tji^es  of  truss  suitable  for,  319 
velocity  of  cages,  323 
Transformers,  312 
Transportation, 

materials  for  miUtary  bridging,  482 
unnecessary,  elimination  of,  366 
Transporter  bridge,  318 
Travel,  automobiles  in  tunnels,  53 
Travelers,  expensive  for  deep  trusses,  176 
Treated  lumber  unsatisfactorj'  for  sidewalks, 

426 
Treated  ties,  economics  of,  182 
Treatment  of  men,  385 
Treatment  of  steel  to  be  encased,  443 
Treatment  of  timber,  183,  l<5l8 
Trestles, 

approaches,  timber,  21 

double-track  railway,  252 

economic  span-lengths,  250-256 

highway,  economic  span-lengths  of,  252 

military  bridges,  467 

pedestal  costs  affecting  economic  layouts. 

252 
reinforced-concrete    for    steam    railways, 

230 
span-iength,  economic,  for  military,  465 
steel,  economics  of,  250-256 

versus  reinforced-concrete,  114 
Triangular  trusses,   divided,   for    continuous 

spans,  78,  SO 
Triangular  versus  Pratt  trussing,  71 
Trimming  and  cutting  metal,  374 
Troubles,  anticipating,  371 
Trough  floors,  182,  214 
Truck  loadings,  125 
Trucks,  great  weight  of,  425 
True  economy,  development  of,  2 
Trunnion  bascules,  290 
Trusses, 

bridges,  economic  span  lengths  for,  150— 

165 
crescent,  272 

criterion  for  alloy  steels,  27,  28 
depths,  economic,  for  parallel  chords,  176 
'depths,  economic,  for  suspension  bridges, 

265 
depths  for  cantilever  bridges,  259 
doubling  of,  21 
economics  of,  175-181 
spacing,  186 
Tullock,  A.  J.,  439 
Tunnels, 

almost      always     more     expensive     than 

bridge,  54 
iiuiinui>l)ilo  travel  in,  53 


INDEX 


511 


Tunnels, 

breakdown  of  vehicles  in,  57 

bridge  costs  compared,  54 

bridges,  comparative  cost  curves  for,  57 

bridges,  comparative  economics,  12,  53 

building  one  pair  of  tubes  at  a  time,  ad- 
vantage of,  54 

carbon-monoxide  gas  in,  53 

cost  of  operation,  55 

cost  of  power,  55  ■ 

depth  of  descent  into,  54 

diameters,  53 

disagreeableness  of  traversing,  54,  56 

Hudson  River,  56 

sanitation,  56 

separation  of  entrances  and  exits,  55 

stoppage  of  traffic,  57 

traffic,  blockade  of,  56 

travel  in,  53 

variation    of    cost,    with    diameters,    53, 
57 

ventilation,  53 
Turning  flanges  of  channels  in,  200,  203 
Twelfth  Street  Trafficway  Viaduct  in  Kansas 

City,  229 
Two-column    versus    four-column    structures 

for  elevated  railroads,  254 
Two-pedestal  piers,  94 
Two-way  versus  one-way  reinforcing  in  slabs, 

220 
Type  A  cantilevers.  86 
Types  of  military  bridges,  464 
Typical  military  bridges,  465 

U 

Unbalanced  wind  pressure,  315 

Unchecked  drawings,  359 

Unclassified  work,  381 

Union  Loop  Elevated  Railroad,  253 

Unit-cost  records,  385 

Unit  prices, 

alloy  steel  constituents,  44 

bridges,  57 

method  of  contract-letting,  340 

various  sections,  205 
Unit  stresses, 

determination,  132 

economics,  125-140 

old  bridges,  415 

limiting,  410,  411 
Unit  wind  loads,  316 
University  of  Kansas,  lectures  on  engineering 

economics,  4 
Unloading  of  materials,  380,  381 
Unnecessary  transportation,   elimination  of, 

366 
Utilization, 

existing  bridges,  480 

local  resources,  480 

machinery  in  shopwork,  202 


Vanadium  steel,  33,  34 

Vancouver,  B.  C,  bridge  painting,  439 

Variation  of  cost  of  tunnels  with  diameters, 

57 
Variations  in  market  price,  effect  of,  23 
Vehicle  for  paint,  best,  435 
Velocity  of  stream,  122 
Ventilation  for  shops,  367,  368 
Ventilation  of  tunnels,  53 
Versed  sine  for  cables,  265,  266 
Vertical-lift  bridges, 

bascule  comparison,  285-287 

bascules,  comparative  economics  of,  302 

base  for  pavement  of,  295 

cantilever  combination,  295 

Duluth,  proposed,  310 

economics,  291-293 

economics  of  detailing,  294 

quantities,  299 

records,  297 

skewed  crossings,  293 

supporting  cables,  295 

swing-span  comparison,  284,  285 

towers,  294 
Viaducts,  217 

economics,  250-256 

erection,  398 

girder  depths,  203 

reinforced  concrete,    water-proofing    for, 
454 
Vibration  and  jigging  of  freshly  made  con- 
crete, 392,  393 
Victory  a  criterion    in   military   bridge   eco- 
nomics, 462 
Visitors  to  drafting  room,  358 
Voids,  volume  of,  in  aggregate,  386 

reduction  of,  389 
Vredenburgh,  Watson,  361 

W 
Waddell  and  Harrington  axle,  291 
Waddell,  Montgomery,  12 
Wages,  flat  scale  of,  370 
Waikato   River  arch   bridge   at   Cambridge, 

N.  Z.,  247 
Waikato  River  arch  bridge  at  Hamilton,  N. 

Z.,  246 
Wakefield  piling,  172 
Waling  frames,  spacing  of,  172 
War, 

effect  of,  on  nickel  price,  33 

engineers  in,  459 

time  element,  460 
Warren  trusses,  economics  of,  179 
Washout  of  falsework,  15 
Waste    not    justified    in    military    bridging; 

463 
Water, 

amount  of,  for  mixing  concrete,  392 


512 


INDEX 


Water, 

depth,  483 

disruptive  force  of,  freezing,  455 
Water-proofing,  189,  390 

concrete  bridges,  451 

cost  of,  450 

definition,  449 

deterioration,  452 

economics,  449-458 

material  for  decks,  183 

material  must  be  elastic,  452 

original  cost,  450 

probable  life,  451 

slabs,  454 

value  of,  452 
Waterway,  clear,  122 

obstruction  of,  by  pier  shafts,  170 
Weakness  in  old  bridges,  414 
Wearing  of  pins,  415,  423 
Wearing  out  of  steel  structures,  423 
Web  splices,  207 
Web  thickness,  207 
Weights, 

alloy-steel  eye-bars  in  suspension-bridges, 
277 

arch   bridges,    approximate   formulee   for, 
248 

arches   compared   to   weights   of   trusses, 
238,  239 

deck  reduced  to  minimum,  194 

metal  in  arches,  formulte  for,  239,  240 

metal  in  cantilever  bridges,  31 

metal  to   carry  one  pound  of  load,   196, 
197 

stiffening  trusses,  93 
Welsh,  Ashbel,  14 

economic  comparison,  14 
West  Point,  Ga.,  crossing  of  the  Chattahoo- 
chee River,  471 
Western  Society  of  Engineers,  90,  112,  268 

paper  presented  to,  150 


Wharves,  384 

Wide  range  of  economic  limits,  16 

Widths, 

decks,  126-128 

footwalks,  128 

roadway  for  militarj-  bridges,  473,  474 

stream,  4S3 

structure    in    cantilever    and    suspension 
bridges,  94 
Wind  loads,  unit,  316 
Wind  pressure, 

bascules,  316 

effect  on  mo^dng  spans,  293 

unbalanced,  315 
Winner  Bridge,  169 
Wolfel,  Paul  L.,  214 
Wood  preservation,  419 
Wooden, 

block  pavements,  426 

piles  versus  reinforced-concrete  pUes,  174 

stringers  undesirable,  425 

ties  for  street  car  traffic,  425 
Work  of  Engineer,  importance  of,  3 
Work,  unclassified,  381 
Working  full  time,  necessity  for,  2 
Working  stresses, 

concrete,  intensities  of,  219 

determination  of,  132 

heat-treated  steel,  37 

old  bridges,  limiting,  410,  411 

tension  and  compression,  lelation  of,  136 
Workmen, 

force  of,  373 

sharing  profits  with,  338,  370 
Worm  gearing,  313 
Wrecks  encountered  in  sinking,  172 
Writings,  author's,  on  bridge  economics,  489 


Yards,  384 
Yates,  J.  J.,  395 


Date  Due 

M/^r'>    ^  f\    iQQ'i 

WK    1  0    lyy^ 

^ 

^1 


BOSTON  COLLEGE 


3  9031    01513706  0 


